MATHEMATICS CLASS X>Chapter 4 - Quadratic Equations>EXERCISE 4.6>Q 15

MEDIUM

10th CBSE

IMPORTANT

Earn 100

Determine the nature of the roots of the following quadratic equation:

$2 (a^{2} + b^{2}) x^{2} + 2 (a + b) x + 1 = 0$

Important Questions on Quadratic Equations

MEDIUM

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 4 - Quadratic Equations>EXERCISE 4.6>Q 15

Determine the nature of the roots of the following quadratic equation:

$(b + c) x^{2} - (a + b + c) x + a = 0$

EASY

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 4 - Quadratic Equations>EXERCISE 4.6>Q 16

Determine the set of values of $k$ for which the following quadratic equation have real roots:

$x^{2} - k x + 9 = 0$

MEDIUM

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 4 - Quadratic Equations>EXERCISE 4.6>Q 16

Determine the set of values of $k$ for which the following quadratic equation have real roots:

$2 x^{2} + k x + 2 = 0$

MEDIUM

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 4 - Quadratic Equations>EXERCISE 4.6>Q 16

Determine the set of values of $k$ for which the following quadratic equation have real roots:

$4 x^{2} - 3 k x + 1 = 0$

MEDIUM

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 4 - Quadratic Equations>EXERCISE 4.6>Q 16

Determine the set of values of $k$ for which the following quadratic equation have real roots:

$2 x^{2} + k x - 4 = 0$

MEDIUM

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 4 - Quadratic Equations>EXERCISE 4.6>Q 17

If the roots of the equation

(b - c) x^{2} + (c - a) x + (a - b) = 0

are equal, then prove that

2 b = a + c

MEDIUM

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 4 - Quadratic Equations>EXERCISE 4.6>Q 18

If the roots of the equation

(a^{2} + b^{2}) x^{2} - 2 (a c + b d) x + (c^{2} + d^{2}) = 0

are equal, prove that

\frac{a}{b} = \frac{c}{d}

.

MEDIUM

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 4 - Quadratic Equations>EXERCISE 4.6>Q 19

If the roots of the equations

a x^{2} + 2 b x + c = 0

and

b x^{2} - 2 \sqrt{a c} x + b = 0

are simultaneously real, then prove that

b^{2} = a c

.