MATHEMATICS CLASS X>Chapter 2 - Polynomials>EXERCISE 2.1>Q 15

MEDIUM

10th CBSE

IMPORTANT

Earn 100

If $α$ and $β$ are the zeros of the quadratic polynomial $f (x) = x^{2} - p (x + 1) - c$ , show that $(α + 1) (β + 1) = 1 - c$ .

Important Questions on Polynomials

MEDIUM

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 2 - Polynomials>EXERCISE 2.1>Q 16

If

α

and

β

are the zeros of a quadratic polynomial such that

α + β = 24

and

α - β = 8

, find the quadratic polynomial having

α

and

β

as its zeros.

MEDIUM

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 2 - Polynomials>EXERCISE 2.1>Q 17

If

α

and

β

are the zeros of the quadratic polynomial

f (x) = x^{2} - 1

, find a quadratic polynomial whose zeros are

\frac{2 α}{β}

and

\frac{2 β}{α}

.

HARD

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 2 - Polynomials>EXERCISE 2.1>Q 18

If

α

and

β

are the zeros of the quadratic polynomial

f (x) = x^{2} - 3 x - 2

, find a quadratic polynomial whose zeros are

\frac{1}{2 α + β}

and

\frac{1}{2 β + α}

MEDIUM

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 2 - Polynomials>EXERCISE 2.1>Q 19

If

α

and

β

are the zeroes of the polynomial

f (x) = x^{2} + p x + q

, form a polynomial whose zeroes are

(α + β)^{2}

and

(α - β)^{2}

.

MEDIUM

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 2 - Polynomials>EXERCISE 2.1>Q 20

If

α

and

β

are the zeros of the quadratic polynomial

f (x) = x^{2} - 2 x + 3,

find a polynomial whose roots are

α + 2, β + 2

.

MEDIUM

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 2 - Polynomials>EXERCISE 2.1>Q 20

If

α

and

β

are the zeros of the quadratic polynomial

f (x) = x^{2} - 2 x + 3,

find a polynomial whose roots are

\frac{α - 1}{α + 1}, \frac{β - 1}{β + 1}

.

MEDIUM

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 2 - Polynomials>EXERCISE 2.1>Q 21

If $α$ and $β$ are the zeroes of the quadratic polynomial $f (x) = a x^{2} + b x + c$ , then evaluate: $α - β$ .

If $α - β = k$ , then find $\frac{\sqrt{b^{2} - 4 a c}}{k}$ ?.

MEDIUM

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 2 - Polynomials>EXERCISE 2.1>Q 21

If

α

and

β

are the zeroes of the quadratic polynomial

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

, and

\frac{1}{α} - \frac{1}{β} = \frac{- \sqrt{b^{2} - 4 kc}}{c}

, find

k

?