CBSE Class 10 Mathematics Quadratic Equations MCQs

Question. The roots of the equation x² + 7x + 10 =0 are
(a) 2 and 5
(b) –2 and 5
(c) –2 and –5
(d) 2 and –5

Question. If α,β are the roots of the quadratic equation x2 + x + 1 = 0, then 1/α + 1/β 
(a) 0
(b) 1
(c) –1
(d) none of these

Question. If the equation x² + 4x + k = 0 has real and distinct roots then
(a) k < 4
(b) k > 4
(c) k ≤ 4
(d) k ≥ 4

Question. If the equation x² – ax + 1 = 0 has two distinct roots then
(a) | a | = 2
(b) | a | < 2
(c) | a | > 2
(d) none of these

Question. If the equation 9x² + 6kx + 4 = 0 has equal roots then the roots are both equal to
(a) ± 2/3
(b) ± 3/2
(c) 0
(d) ± 3

Question. If the equation (a² + b²)x² – 2b(a + c)x + b² + c² = 0 has equal roots then 
(a) 2b = a + c
(b) b² = ac
(c) b = 2ac/a+c
(d) b = ac

Question. If the equation x² – bx + 1 = 0 has two distinct roots then
(a) –3 < b < 3
(b) –2 < b < 2
(c) b > 2
(d) b < –2

Question. If x = 1 is a common root of the equations ax² + ax + 3 = 0 and x² + x + b = 0 then ab =
(a) 6
(b) 3
(c) –3
(d) 7/2

Question. If p and q are the roots of the equation x² – px + q = 0, then
(a) p = 1, q = –2
(b) p = –2, q = 0
(c) b = 0, q = 1
(d) p = –2, q = 1

Question. If the equation ax² + bx + c = 0 has equal roots then c =
(a) -b/2a
(b) b/2a
(c) -b²/4a
(d) b²4a

Question. If a and b can take values 1, 2, 3, 4. Then the number of the equations of the form ax²+ bx + c = 0 having real roots is
(a) 6
(b) 7
(c) 10
(d) 12

Question. The number of quadratic equations having real roots and which do not change by squaring their roots is
(a) 4
(b) 3
(c) 2
(d) 1

Question. If one of the roots of the quadratic equation (k² + 4)x² + 13x + 4k is reciprocal of the other then k =
(a) 2
(b) 1
(c) –1
(d) – 2

Question. If α,β  are the roots of the quadratic equation x² – p(x + 1) – c = 0, then (α+1 )(β+1) =
(a) c – 1
(b) 1 – c
(c) c
(d) 1 + c

Question. Find the values of k for which the quadratic equation 2x² + kx + 3 = 0 has real equal roots.
(a) ±2 √6
(b) 2√ 6
(c) 0
(d) ±2

Question. Find the values of k for which the quadratic equation kx(x – 3) + 9 = 0 has real equal roots.
(a) k = 0 or k = 4
(b) k = 1 or k = 4
(c) k = –3 or k = 3
(d) k = –4 or k = 4

Question. Find the values of k for which the quadratic equation 4x² – 3kx + 1 = 0 has real and equal roots.
(a) ±4/3
(b) ±2/3
(c) ±2 
(d) none of these

Question. Find the values of k for which the quadratic equation (k – 12)x2 + 2(k – 12)x + 2 = 0 has real and equal roots.
(a) k = 0 or k = 14
(b) k = 12 or k = 24
(c) k = 14 or k = 12
(d) k = 1 or k = 12

Question. Find the values of k for which the quadratic equation k²x² – 2(k – 1)x + 4 = 0 has real and equal roots.
(a) k = 0 or k = 1/3
(b) k = 1 or k = 1/3
(c) k = –1 or k = 1/3
(d) k = –3 or k = 1/3

Question. If –4 is a root of the equation x² + px – 4 = 0 and the equation x² + px + q = 0 has equal roots, find the value of p and q.
(a) p =3, q = 9
(b) p =9, q = 3
(c) p = 3, q = 4/9
(d) p = 3, q = 9/4

Question. If the roots of the equation (a – b)x² + (b – c)x + (c – a) = 0 are equal, then b + c =
(a) 2a
(b) 2bc
(c) 2c
(d) none of these

Question. Find the positive value of k for which the equations x² + kx + 64 = 0 and x² – 8x + k = 0 will have real roots.
(a) 8
(b) 16
(c) –8
(d) –16

Question. The sum of a number and its reciprocal is 10/3. Find the number.
(a) 3
(b) 1/3
(c) both (a) and (c)
(d) none of these

Question. Divide 12 into two parts such that the sum of their squares is 74.
(a) 7 and 5
(b) 8 and 4
(c) 10 and 2
(d) none of these

Question. The sum of the squares of two consecutive natural numbers is 421. Find the numbers.
(a) 14 and 5
(b) 14 and 15
(c) 10 and 5
(d) none of these

Question. The sum of two numbers is 15 and the sum of their reciprocals is 3/10. Find the numbers.
(a) 14 and 5
(b) 14 and 15
(c) 10 and 5
(d) none of these

Question. Divide 12 into two parts such that their product is 32.
(a) 7 and 5
(b) 8 and 4
(c) 10 and 2
(d) none of these

Question. The value of k for which equation 9x² + 8xk + 8 = 0 has equal roots is:
(a) only 3
(b) only –3
(c) ±3
(d) 9

Question. Which of the following is not a quadratic equation?
(a) x-3/x = 4
(b) 3x-5/x = x²
(c) x = 3/2
(d) x = –3

Question. Which of the following is a solution of the quadratic equation 2x2 + x – 6 = 0?
(a) x = 2
(b) x = –12
(c) x = 3/2
(d) x = –3

Question. The value of k for which x = –2 is a root of the quadratic equation kx² + x – 6 = 0
(a) –1
(b) –2
(c) 2
(d) -3/2

Question. The value of p so that the quadratics equation x2 + 5px + 16 = 0 has no real root, is
(a) p>8
(b) p<5
(c) -8/5<x< 8/5
(d) -8/5 ≤x< = 0

Question. If px2 + 3 w + q = 0 has two roots x = –1 and x = –2, the value of q – p is
(a) –1
(b) –2
(c) 1
(d) 2

Question. The common root of the quadratic equation x² – 3x + 2 = 0 and 2x² – 5x + 2 = 0 is:
(a) x = 2
(b) x = –2
(c) x = 1/2
(d) x = 1

Question. If x² – 5x + 1 = 0, the value of (x+1/x) is:
(a) –5
(b) –2
(c) 5
(d) 3

Question. If a – 3 = 10/a , the value of a are
(a) –5, 2
(b) 5, –2
(c) 5, 2
(d) 5, 0

Question. If the roots of the quadratic equation kx2 + (a + b)x + ab = 0 are (–1, –b), the value of k is:
(a) –1
(b) –2
(c) 1
(d) 2

Question. The quadratic equation with real coefficient whose one root is 2+ √ 3 is:
(a) x² – 2x + 1 = 0
(b) x² – 4x + 1 = 0
(c) x² – 4x + 3 = 0
(d) x² – 4x + 4 = 0

Question. If the difference of roots of the quadratic equation x² + kx + 12 = 0 is 1, the positive value of k is:
(a) –7
(b) 7
(c) 4
(d) 8