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

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10th CBSE

IMPORTANT

Earn 100

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.

Important Questions on Polynomials

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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}

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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}

.

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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

.

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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}

.

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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 $\frac{\sqrt{b^{2} - 4 a c}}{k}$ ?.

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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

?

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} - 2 α β = - (\frac{b}{c} + \frac{2 k}{a})

, then find

k ?