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

MEDIUM

10th CBSE

IMPORTANT

Earn 100

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

Important Questions on Quadratic Equations

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.

MEDIUM

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 4 - Quadratic Equations>Exercise 4E>Q 2

The sum of natural number and its positive square root is

132

. Find the number.

MEDIUM

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 4 - Quadratic Equations>Exercise 4E>Q 3

The sum of two natural number is $28$ and their product is $192$ . Find the numbers.

MEDIUM

10th CBSE

IMPORTANT

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

The sum of the squares of two consecutive positive integers is

365

. Find the integers.

HARD

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 4 - Quadratic Equations>Exercise 4E>Q 5

The sum of the squares of two consecutive positive odd numbers is

514

. Find the numbers.

MEDIUM

10th CBSE

IMPORTANT

Secondary School Mathematics for Class 10>Chapter 4 - Quadratic Equations>Exercise 4E>Q 6

The sum of the squares of two consecutive positive even numbers is

452

. Find the numbers.