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This mock test of Quadratic Equations - Olympiad Level MCQ, Class 10 Mathematics for Class 10 helps you for every Class 10 entrance exam.
This contains 25 Multiple Choice Questions for Class 10 Quadratic Equations - Olympiad Level MCQ, Class 10 Mathematics (mcq) to study with solutions a complete question bank.
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QUESTION: 1

The roots of the equation (x – a) (x – b) + (x – b) (x – c) + (x – c) (x – a) = 0 are :

Solution:

QUESTION: 2

Solution of a quadratic equation x^{2}+ 5x - 6 = 0

Solution:
X^2 +5x-6=0

=x^2+6x-x-6=0[by splitting middle term]

=x(x+6)-1(x+6)

=(x-1)(x+6)

x=1;x=-6

QUESTION: 3

If the sum of p terms of an A.P. is q and the sum of q terms is p, then the sum of (p + q) terms will be

Solution:

The sum of first p term of AP is q, which means that the number of terms is p

Thereby, let us take the first term as A and the common difference d

The sum of first q term of AP is p, which means that the number of terms is q

Thereby, let us take the first term as A and the common difference d

Therefore, the sum

Subtracting the sum of the term , p and q

After solving the equation we get the value of d as

Now with , first value of the series is a and the number of terms is

**Therefore, the sum is **

QUESTION: 4

If α,β are the roots of the equation x^{2} + 2x + 4 = 0, then is equal to :

Solution:

QUESTION: 5

If then :

Solution:

QUESTION: 6

If α, β are the roots of the equation x^{2} + 7x + 12 = 0, then the equation whose roots are (α + β)^{2} and (α – β)^{2} is:

Solution:

QUESTION: 7

The value of k (k > 0) for which the equations x^{2} + kx + 64 = 0 and x^{2} – 8x + k = 0 both will have real roots is :

Solution:

Let D₁ and D₂ be the discriminant of the given equations and these will have equal roots only if D₁, D₂ ≥ 0

Or, if D₁ = (k² -4 × 64) ≥ 0 and D₂ = (64 - 4k) ≥ 0

Or, if k² ≥ 256 and 4k ≤ 64

Or, if k ≥ 16 and k ≤ 16

Or, k = 16

Hence the positive value of k is 16.

QUESTION: 8

If α,β are roots of the quadratic equation x^{2} + bx – c = 0, then the equation whose roots are b and c is

Solution:

QUESTION: 9

Solve for y : 9y^{4} – 29y^{2} + 20 = 0

Solution:

QUESTION: 10

Solve for x : x^{6} – 26x^{3} – 27 = 0

Solution:

QUESTION: 11

If 7th and 13th term of an A.P. are 34 and 64 respectively, then its 18th term is

Solution:

QUESTION: 12

Solve : – = 3

Solution:

QUESTION: 13

Solve for x : :

Solution:

QUESTION: 14

Solve x : :

Solution:

QUESTION: 15

Solve for x : – x + 2 = , x ε R :

Solution:

QUESTION: 16

Solve for x : 3^{x+2} + 3^{-x} = 10

Solution:

QUESTION: 17

Solve for x : (x + 1) (x + 2) (x + 3) (x + 4) = 24 (x ε R) :

Solution:

QUESTION: 18

The sum of all the real roots of the equation |x – 2|^{2} + |x – 2| – 2 = 0 is :

Solution:

QUESTION: 19

If a, b ε {1, 2, 3, 4}, then the number of quadratic equations of the form ax^{2} + bx + 1 = 0, having real roots is :

Solution:

QUESTION: 20

The number of real solutions of x – is :

Solution:

QUESTION: 21

Ifthen x is equal to :

Solution:

QUESTION: 22

The quadratic equation 3x^{2} + 2(a^{2} + 1) x + a^{2} – 3a + 2 = 0 possesses roots of opposite sign then a lies in:

Solution:

QUESTION: 23

The equation has :

Solution:

QUESTION: 24

The number of real solutions of the equation 2|x|^{2} – 5|x| + 2 = 0 is :

Solution:

QUESTION: 25

The number of real roots of the equation (x – 1)^{2} + (x – 2)^{2} + (x – 3)^{2} = 0 :

Solution:

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