MATHEMATICS CLASS X>Chapter 2 - Polynomials>EXERCISE 2.1>Q 12

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10th CBSE

IMPORTANT

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If $α$ and $β$ are the zeros of the quadratic polynomial $p (s) = 3 s^{2} - 6 s + 4$ , find the value of $\frac{α}{β} + \frac{β}{α} + 2 (\frac{1}{α} + \frac{1}{β}) + 3 α β$ .

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Important Questions on Polynomials

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10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 2 - Polynomials>EXERCISE 2.1>Q 13

If the squared difference of the zeros of the quadratic polynomial $f (x) = x^{2} + p x + 45$ is equal to $144$ find the value of $p$ .

If $p = \pm k$ , then find $k$ ?

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10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 2 - Polynomials>EXERCISE 2.1>Q 14

If

α

and

β

are the zeros of the quadratic polynomial

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

, prove that

\frac{α^{2}}{β^{2}} + \frac{β^{2}}{α^{2}} = \frac{p^{4}}{q^{2}} - \frac{4 p^{2}}{q} + 2

.

MEDIUM

10th CBSE

IMPORTANT

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

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

.

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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.

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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

.