Secondary School Mathematics for Class 10>Chapter 4 - Quadratic Equations>Exercise 4D>Q 19

EASY

10th CBSE

IMPORTANT

Earn 100

Find the values of $k$ for which the given quadratic equation has real and distinct roots:
$k x^{2} + 6 x + 1 = 0$

Important Questions on Quadratic Equations

EASY

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 4 - Quadratic Equations>Exercise 4D>Q 19

Find the values of $k$ for which the given quadratic equation has real and distinct roots:

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

EASY

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 4 - Quadratic Equations>Exercise 4D>Q 19

Find the values of

k

for which the given quadratic equation has real and distinct roots:

9 x^{2} + 3 k x + 4 = 0

EASY

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 4 - Quadratic Equations>Exercise 4D>Q 19

Find the values of

k

for which the given quadratic equation has real and distinct root:

5 x^{2} - k x + 1 = 0

MEDIUM

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 4 - Quadratic Equations>Exercise 4D>Q 20

If

a

and

b

are real and

a \neq b

then show that the roots of the equation

(a - b) x^{2} + 5 (a + b) x - 2 (a - b) = 0

are real and unequal.

MEDIUM

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 4 - Quadratic Equations>Exercise 4D>Q 21

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

Secondary School Mathematics for Class 10>Chapter 4 - Quadratic Equations>Exercise 4D>Q 21

If

a d \neq b c

then prove that the equation

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

has no real roots.

MEDIUM

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 4 - Quadratic Equations>Exercise 4D>Q 22

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

MEDIUM

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 4 - Quadratic Equations>Exercise 4E>Q 1

The sum of a natural number and its square is

156

. Find the number.