### Quadratic Equations Test:

**Ques: **The roots of the equation ix^{2} – 4x – 4i = 0 are

(a) –2i

(b) 2i

(c) –2i, –2i

(d) 2i, 2i

Ans. (c)

Related: probability question examples

**Ques: **If sin A, sin B, cos A are in G.P., then roots of x^{2} + 2x cot B + 1 = 0 are always

(a) Real

(b) Imaginary

(c) Greater than 1

(d) Equal

Ans. (a)

**Ques: **The roots of the quadratic equation 2x^{2} + 3x + 1 = 0, are

(a) Irrational

(b) Rational

(c) Imaginary

(d) None of these

Ans. (b)

**Ques: **If a root of the equation x^{2} + px + 12 = 0 is 4, while the roots of the equation x^{2} + px + q = 0 are same, then the value of q will be

(a) 4

(b) 4/49

(c) 49/4

(d) None of these

Ans. (c)

Related: Mensurations formulas questions

**Ques: **Roots of the equation x^{2} + bx – c = 0 (b, c > 0) are

(a) Both positive

(b) Both negative

(c) Of opposite sign

(d) None of these

Ans. (c)

**Ques: **If the sum of the roots of the equation ax^{2} + bx + c = 0 be equal to the sum of their squares, then

(a) a(a + b) = 2bc

(b) c(a + c) = 2ab

(c) b(a + b) = 2ac

(d) b(a + b) = ac

Ans. (c)

**Ques: **If the roots of equation 5x^{2} – 7x + k = 0 are reciprocal to each other, then value of k is

(a) 5

(b) 2

(c) 1/5

(d) 1

Ans. (a)

Related: HCF and LCM word problems

**Ques: **The roots of the equation x^{2/3} + x^{1/3} – 2 = 0 are

(a) 1, 4

(b) 1, –4

(c) 1, –8

(d) 1, 8

Ans. (c)

**Ques: **The expression y = ax^{2} + bx + c has always the same sign as c if

(a) 4ac < b^{2}

(b) 4ac > b^{2
}(c) ac < b^{2}

(d) ac > b^{2}

Ans. (b)

**Ques: **If the roots of x^{2} – bx + c = 0 are two consecutive integers, then b^{2} – 4c is

(a) 1

(b) 2

(c) 3

(d) 4

Ans. (a)

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**Ques: **If one of the roots of equation x^{2} + ax + 3 = 0 is 3 and one of the roots of the equation x^{2} + ax + b = 0 is three times the other root, then the value of *b* is equal to

(a) 3

(b) 4

(c) 2

(d) 1

Ans. (a)

**Ques: **If the roots of the equation ax^{2} + bx + c = 0 are reciprocal to each other, then

(a) a – c = 0

(b) b – c = 0

(c) a + c = 0

(d) b + c = 0

Ans. (a)

**Ques: **The number which exceeds its positive square root by 12 is

(a) 9

(b) 16

(c) 25

(d) None of these

Ans. (b)

Related: Ratio and proportions problems

**Ques: **What is the sum of the squares of roots of x^{2} – 3x + 1 = 0

(a) 5

(b) 7

(c) 9

(d) 10

Ans. (b)

**Ques. **In the equation x^{3} + 3Hx + G = 0, if *G* and *H* are real and G^{2} + H^{3} > 0, then the roots are

(a) All real and equal

(b) All real and distinct

(c) One real and two imaginary

(d) All real and two equal

Ans. (c)

**Ques: **Roots of ax^{2} + b = 0 are real and distinct if

(a) ab > 0

(b) ab < 0

(c) a, b > 0

(d) a, b < 0

Ans. (b)

**Ques: **If x^{2} + y^{2} = 25, xy = 12, then x =

(a) {3, 4}

(b) {3, –3}

(c) {3, 4, –3, –4}

(d) {–3, –3}

Ans. (c)

Related: Average problems for practice

**Ques: **If the roots of equation x^{2} + px + q = 0 differ by 1, then

(a) p^{2} = 4q

(b) p^{2} = 4q + 1

(c) p^{2} = 4q – 1

(d) None of these

Ans. (b)

**Ques. **Two students while solving a quadratic equation in *x*, one copied the constant term incorrectly and got the roots 3 and 2. The other copied the constant term and coefficient of x^{2 }correctly as –6 and 1 respectively. The correct roots are

(a) 3, –2

(b) –3, 2

(c) –6, –1

(d) 6, –1

Ans. (d)

**Ques: **If x be real, then the minimum value of x^{2} – 8x + 17 is

(a) –1

(b) 0

(c) 1

(d) 2

Ans. (c)

**Ques: **Roots of the equations 2x^{2} – 5x + 1 = 0, x^{2} + 5x + 2 = 0 are

(a) Reciprocal and of same sign

(b) Reciprocal and of opposite sign

(c) Equal in product

(d) None of these

Ans. (b)

Related: arithmetic operation questions and answers

**Ques: **The number of solutions of log_{4} (x – 1) = log_{2} (x – 3)

(a) 3

(b) 1

(c) 2

(d) 0

Ans. (b)

**Ques. **If the quadratic equations ax^{2} + 2cx + b = 0 and ax^{2} + 2bx + c = 0 have a common root, then a + 4b + 4c =

(a) –2

(b) –1**
**(c) 0

(d) 1

Ans. (c)

**Ques: **If one root of ax^{2} + bx + c = 0 be square of the other, then the value of b^{3} + ac^{2} + a^{2}c is

(a) 3abc

(b) –3abc

(c) 0

(d) None of these

Ans. (a)

**Ques: **If x^{2} + px + 1 is a factor of the expression ax^{3} + bx + c, the

(a) a^{2} + c^{2} = –ab

(b) a^{2} – c^{2} = –ab

(c) a^{2} – c^{2} = ab

(d) None of these

Ans. (c)

Related: Percentage questions

**Ques: **The number of roots of the equation | x |^{2} – 7 | x | + 12 = 0 is

(a) 1

(b) 2

(c) 3

(d) 4

Ans. (d)

**Ques. **The number of quadratic equations which remains unchanged by squaring their roots is

(a) 2

(b) 4

(b) 6

(d) Infinite many

Ans. (a)

**Ques: **The number of solutions for the equation x^{2} – 5 | x | + 6 = 0 is

(a) 4

(b) 3

(c) 2

(d) 1

Ans. (a)

**Ques: **Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic equation

(a) x^{2} – 18x – 16 = 0

(b) x^{2} – 18x + 16 = 0

(c) x^{2} + 18x – 16 = 0

(d) x^{2} + 18x + 16 = 0

Ans. (b)

Related: Quadrilaterals questions

**Ques: **If a + b + c = 0, then the roots of the equation 4x^{2} + 3bx + 2c = 0 are

(a) Equal

(b) Imaginary

(c) Real

(d) None of these

Ans. (c)

**Ques: **If the roots of the equation x^{2} + 2mx + m^{2} – 2m + 6 = 0 are same, then the value of *m* will be

(a) 3

(b) 0

(c) 2

(d) –1

Ans. (a)

**Ques. **The number of values of for which the equation x^{2} – 3x + k = 0 has two real and distinct roots lying in the interval (0, 1), are

(a) 0

(b) 2

(c) 3

(d) Infinitely many

Ans. (a)

**Ques: **Product of real roots of the equation t^{2}x^{2} + | x | + 9 = 0

(a) Is always positive

(b) Is always negative

(c) Does not exist

(d) None of these

Ans. (c)

Related: Polynomials questions

**Ques: **The equation e^{x} – x – 1 = 0 has

(a) Only one real root x = 0

(b) At least two real roots

(c) Exactly two real roots

(d) Infinitely many real roots

Ans. (a)

**Ques: **If the product of roots of the equation, mx^{2} + 6x + (2m – 1) = 0 is –1, then the value of *m* will be

(a) 1

(b) – 1

(c) 1/3

(d) – 1/3

Ans. (c)

**Ques: **The value of k for which 2x^{2} – kx + x + 8 = 0 has equal and real roots are

(a) –9 and –7

(b) 9 and 7

(c) –9 and 7

(d) 9 and –7

Ans. (d)

**Ques: **The roots of 4x^{2} + 6px + 1 = 0 are equal, then the value of *p* is

(a) 4/5

(b) 1/3

(c) 2/3

(d) 4/3

Ans. (c)