MCQ Questions on Quadratic Equations for Class 10

MCQ Questions on Quadratic Equations for Class 10 – Maths Class 10 MCQ Online Test are covered in this Article. Quadratic Equations Class 10 MCQ Test contains 30 questions. Answers to MCQs on Quadratic Equations Class 10 MCQ with Answers Maths are available at the end of the last question. These MCQ have been made for Class 10 students to help check the concept you have learnt from detailed classroom sessions and application of your knowledge.

Board CBSE
Textbook Maths (NCERT)
Class Class 10
Chapter Chapter 4 Quadratic Equations
Category MCQ Questions for Class 10 Maths with Answers

MCQ Questions on Quadratic Equations for Class 10 – Maths Class 10 MCQ Online Test

Ques1. Which of the following is the standard form of quadratic equation

(a)ax²+bx+c=0
(b)bx+ax²+c=0
(c)ax²+c+bx=0
(d)c+ax²+bx=0

Ques2. The degree of a quadratic equation is

(a)1
(b)2
(c)3
(d)0

Ques3. Which of the following is not a quadratic equation

(a)(x+1)² =4
(b) (x+1) (x+2) =(x-3)2x
(c) (x+2) (x-2) =(x-1)²
(d) x+1=x²

Ques4. The roots of the quadratic equation x²-5x+4=0 are

(a)1,4
(b)2,2
(c)2,√2
(d)1,5




Ques5. Which of the following is quadratic formula for ax²+bx+c=0, where b²-4ac≥0

(a)(-b± √b²-4ac) / 2a
(b) (-b±√b²-4ac) / 2
(c) (b±√b²-4ac) / 2
(d) (-b±√b²-4c) / 2a

Ques6. Roots of the quadratic equation 3x²-5x+1=0 are

(a)3,2
(b) 5+√13 / 6, 5-√13 / 6
(c) -5-√13 / 6,-5-√13 / 6
(d) 5±√13 / 2,-5±√13 / 2

Ques7. Discriminant of quadratic equation ax²+bx+c=0 is

(a) b²-4ac
(b) -b±√b²-4ac / 2a
(c) b²-4c
(d) b²-4a

Ques8. A quadratic equation ax²+bx+c=0 has distinct real roots if

(a)b²-4ac=0
(b) b²-4ac<0
(c) b²-4ac >0
(d)b²-4ac≠0

Ques9. Discriminant of the quadratic equation is x²+6x-60=0 is

(a)204
(b)276
(c)240
(d)286

Ques10. Find the value of k, if the quadratic equation x²-4kx+36=0 has two equal real roots

(a)k=1
(b)k=2
(c)k=3
(d)k=4

MCQ Questions on Quadratic Equations for Class 10 – Maths Class 10 MCQ Online Test

Ques11. The roots of the quadratic equation x + 1/x = 2, x ≠0 are

(a)1,1
(b) -1,1
(c)2,2
(d)1,2

Ques12.The product of the roots of the quadratic equation 3x² – 2x +7 =0 is

(a)2/3
(b) 7/3
(c)-7/3
(d)-2/3

Ques13. If one root of the equation x² +mx -60 =0 is 4, while the equation x² +mx +n =0 has equal roots , then the value of n is

(a)11
(b)4
(c) 4/121
(d)121/4

Ques14. The sum of the roots of the quadratic equation √2x² – 2√2x +7 =0 is

(a)2/√2
(b) 2
(c) -√2/2
(d) None




Ques15. p and q are two roots of the quadratic equation 2x² +5x +2=0, then the value of 1/p+1/q is

(a)0
(b) 1
(c)-5/2
(d)-2/5

Ques16. A quadratic equation ax²+bx+c=0 has no real roots if

(a)b²-4ac=0
(b)b²-4ac<0
(c) b²-4ac >0
(d)b²-4ac≠0

Ques17. For the quadratic equation x²-9x+10=0, what will be the discriminant and nature of roots

(a)81 and distinct roots
(b) -81 and no real roots
(c) 41 and distinct roots
(d) -41 and equal roots

Ques18. If -10 is a root of the equation x² +px-20 =0, then p is

(a)-8
(b)10
(c)5
(d)8

Ques19. Number of real roots the equation (x-1)² – x² =0 has

(a)0
(b)1
(c)2
(d)3

Ques20. Which of the following quadratic equations has -1 as a root

(a)x² +10x-20 =0
(b) x² +x+1 =0
(c) x² -x-2 =0
(d) x² =0

MCQ Questions on Quadratic Equations for Class 10 – Maths Class 10 MCQ Online Test

Ques21. Which of the following has sum of its roots as 5√3

(a) √2x² +7√2x+3 =0
(b) -x² +5√3x+1 =0
(c) x² +5√3x+120 =0
(d) √3x² -5√3x+1=0

Ques22. The quadratic equation -9x² +5√7x-1 =0 has

(a)two distinct real roots
(b)two equal roots
(c)no real roots
(d)more than two real roots

Ques23. If one root of the equation 12x² +5x-(k+3) =0 is reciprocal of the other. The value of k is

(a)15
(b)-15
(c)9
(d)-9

Ques24. The maximum number of roots for a quadratic equation is

(a)1
(b)2
(c)3
(d)4

Ques25. If x² +px+9 =0 has no real roots then

(a)  -6 <p<6
(b)  p<6
(c)  p>6
(d) None of these

Ques26. If sum of roots of a quadratic equation is -5 and product of roots is 18. Then the equation is

(a)x² +5x+18 =0
(b) x² +√3x+10 =0
(c) 5x² +25x+90 =0
(d) 5x² -25x+90 =0

Ques27. If α and β are two roots of the equations x² +8x+15 =0. Then value of √αβ +1 is

(a) √15 +1
(b) √(-15) +1
(c) √5 +1
(d) 15

Ques28. The roots of the quadratic equation x² -16 =0 are

(a)both positive
(b) both negative
(c)one positive and one negative
(d) None of these

Ques29. If roots of the quadratic equation x² -mx+n =0 are 9 and -2, then

(a)m=-7, n =10
(b) m=-18, n =7
(c) m=-11, n =18
(d) m=7, n =-18

Ques30. If α and β are two roots of the equations x² +x+1/4 =0. Then value of (α – β)αβ is

(a) 0
(b)-1/4
(c) 1
(d) 1/4




MCQ Questions on Quadratic Equations for Class 10 – Maths Class 10 MCQ Online Test

Correct Answers with Solutions

1. Correct option (a)

Sol: ax²+bx+c=0 is the standard form of a quadratic equation

2. Correct option (b)

Sol:  A quadratic equation ax²+bx+c=0 has degree 2.

3. Correct option (c)

Sol: (x+2) (x-2) =(x-1)²
x²-4=x²-2x+1
2x-1-4=0
2x-5=0
It is not of the form ax²+bx+c=0.So, it is not a quadratic equation.

4. Correct option (a)

Sol:  x²-5x+4=0
x²-4x-x+4=0
x (x-4)- (x-4) =0
(x-4) (x-1) =0
x = 4 and x = 1

5. Correct option (a)

Sol:  Formula for finding the roots of a quadratic equation ax²+bx+c=0 is -b±√b²-4ac / 2a , provided b²-4ac≥0 and it is known as Quadratic formula.

6. Correct option(b)

Sol:  Comparing with standard form of quadratic equation
a = 3, b = -5 and c =1
x = -b±√b²-4ac / 2a
x = -(-5)±√(-5)²-4(3)(1) / 2(3)
x = 5±√25-12 / 2(3)
x = 5±√13 / 6
x = 5+√13 / 6 and x = 5-√13 / 6

7. Correct option (a)

Sol: b²-4ac is known as discriminant of quadratic equation ax²+bx+c=0.

8. Correct option (c)

Sol:   A quadratic equation ax²+bx+c=0 has distinct real roots if b²-4ac >0

9. Correct option (b)

Sol:   Comparing with standard form of quadratic equation a = 1, b = 6 and c = -60
b²-4ac = (6)² – 4(1) (-60) = 36+240 = 276

10. Correct option (c)

Sol: Comparing with standard form of quadratic equation a = 1, b = -4k and c = 36
And the condition for real and equal roots is b²-4ac=0
(-4k)² – 4(1)(36) =0
16k² – 144 = 0
16k² = 144
k² = 9
k = 3




11. Correct option(a)

Sol: We have,
x + 1/x = 2
(x²+1)/x =2
x²+1 = 2x
x² – 2x +1 =0
x²–x-x +1 =0
x (x-1)-1(x-1) = 0
(x-1) (x-1) =0
x = 1 ,1

12. Correct option (b)

Sol: Comparing with standard form of quadratic equation a = 3, b = -2 and c = 7
Product of the roots = c/a = 7/3

13. Correct option (d)

Sol: Since 4 is a root of x² +mx -60 =0, it will satisfy the equation
(4)² +m (4)-60=0
16+4m-60=0
4m = 44
m = 11
Now, roots of the equation x² +mx +n =0 are equal
x² +11x +n =0
the condition for real and equal roots is b²-4ac=0
(11)² – 4(1) (n)=0
121 = 4n
n = 121/4

14. Correct option (b)

Sol: Comparing with standard form of quadratic equation a = √2, b = -2√2 and c = 7
Sum of the roots = -b/a =-(-2√2)√2 =2

15. Correct option (c)

Sol: Sum of the roots =p+q= -b/a= -5/2
Product of the roots =pq= c/a=2/2=1
1/p + 1/q = (p+q)/pq = (-5/2)/1=-5/2

MCQ Questions on Quadratic Equations for Class 10 – Maths Class 10 MCQ Online Test

16. Correct option (b)

17. Correct option(c)

Sol: Comparing with standard form of quadratic equation a = 1, b = -9 and c = 10
b²-4ac = (-9)² – 4(1)(10) = 81-40 = 41 >0
Nature of roots is real and distinct.

18. Correct option(d)

Sol: Since -10 is a root of x² +px -20 =0, it will satisfy the equation
(-10)²+p (-10)-20=0
100 – 10p-20=0
10p = 80
p = 8

19. Correct option(b)

Sol: (x-1)² – x² =0
x²-2x+1- x²=0
2x=1
x = ½
The equation has one real root.

20. Correct option(c)

Sol: If -1 is a root of the equation then it will satisfy the quadratic equation
x²-x-2 =0
LHS = (-1)² – (-1)-2 = 1+1-2 = 0 =RHS




21. Correct option(b)

Sol: -x² +5√3x+1 =0, Here a = -1, b=5√3 , c =1
Sum of roots = -b/a= -(5√3)/-1 =5√3

22. Correct option(a)

Sol: -9x² +5√7x-1 =0
Here, a = -9, b = 5√7, c = -1
b²-4ac = (5√7)² – 4(-9) (-1) = 175-36=139>0
Hence, the quadratic equation has two distinct real roots.

23. Correct option(b)

Sol: Let one root of the equation is m. If one root is reciprocal of other, then product of roots will be
m × 1/m  = c/a = -(k+3)/12
1 = -(k+3)/12
-k-3 = 12
-k = 15 or k = -15

24. Correct option (b)

Sol:: Since the degree of quadratic equation is 2, so maximum number of roots are 2.

25. Correct option(a)

Sol: Given, x² +px+9 =0 has no real roots. Here, a = b²-4ac <0
(p)² – 4(1)(9) <0
P² <36
-6 <p<6

26. Correct option (c)

Sol: Sum of roots =  -b/a =  -25/5  = -5
Product of roots =  c/a =  90/5 = 18
So, the equation is 5x² +25x+90 =0

27. Correct option(a)

Sol:  α and β are two roots of the equations x² +8x+15 =0
x² +8x+15 =0
x² +5x+3x+15 =0
x(x+5) +3(x+5) =0
(x+5) (x+3) =0
x = -5, -3
Let α = -5 and β = -3
Then, (√αβ) +1 = (√-5-3)+1
= √15 +1

28. Correct option (c)

Sol: x² -16 =0
x² = 16
x = ±4
Hence, one roots is positive and other one is negative.

29. Correct option (d)

Sol:  Let a = 9 and β = -2
Sum of the roots = a + β = -b/a=-(-m)/1
9 + (-2) = m
m = 7

Product of roots = a × β =c/a =n/1
9(-2) = n
n = -18

30. Correct option(a)

Sol:  a and β are two roots of the equations x² +x+14 =0
x² +x+1/4 =0
(x+1/2 )² = 0
(x+1/2) (x+1/2 )=0
x = -1/2 , -1/2

Let a = -1/2 and β = -1/2
Then, (α-β)aβ =( -1/2-( -1/2 )) ×( -1/2 )( -1/2)
= (-1/2+ 1/2) × (1/4) =0

 

MCQ Questions for Class 10 Maths

NCERT Solutions for Class 10

CBSE Notes for Class 10

MCQ Questions for Class 10

Leave a Comment