All In One ICSE Mathematics Class 10>Chapter 5 - Quadratic Equations in One Variable>Topic Exercise>Q 8

MEDIUM

10th ICSE

IMPORTANT

Earn 100

If the roots of the equation $(b - c) x^{2} + (c - a) x + (a - b) = 0$ are equal, then prove that $2 b = a + c$ .

Important Questions on Quadratic Equations in One Variable

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 5 - Quadratic Equations in One Variable>Topic Exercise>Q 9

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 show that

b^{2} = a c

.

HARD

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 5 - Quadratic Equations in One Variable>Topic Exercise>Q 10

If the roots of the equation

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

are equal, prove that either

a = 0 o r a^{3} + b^{3} + c^{3} = 3 a b c

.

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 5 - Quadratic Equations in One Variable>Topic Exercise>Q 11

If

p, q, r & s

are real numbers such that

p r = 2 (q + s)

, then show that at least one of the equations

x^{2} + p x + q = 0 a n d x^{2} + r x + s = 0

has real roots.

HARD

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 5 - Quadratic Equations in One Variable>Topic Exercise>Q 12

Prove that both the roots of the equation

(x - a) (x - b) + (x - b) (x - c) + (x - c) (x - a) = 0

are real but they are equal only which

a = b = c

.

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 5 - Quadratic Equations in One Variable>Topic Exercise>Q 1

The sum of the squares of two consecutive natural numbers is

481

. Find the sum of two numbers.

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 5 - Quadratic Equations in One Variable>Topic Exercise>Q 2

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

290

. Find them.

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 5 - Quadratic Equations in One Variable>Topic Exercise>Q 3

Divide

25

into two parts, such that twice the square of the larger part exceeds thrice the square of the smaller part by

29

.

HARD

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 5 - Quadratic Equations in One Variable>Topic Exercise>Q 4

The sum of two numbers is

18

. If the sum of their reciprocals is

\frac{1}{4}

, if the numbers are

k, 2 k

then find the value of

k

.