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Polynomials

Long Answer Type

421. Find a quadratic polynomial whose zeroes are 1 and (-3). Verify the relation between the coefficients and zeroes of the polynomial.

2920 Views

422. Find the zeroes of the quadratic polynomial 4x² – 4x – 3 and verify the relation between the zeroes and its coefficients.

3023 Views

423. If α and β are the zeroes of the polynomial ax² + bx + c then find
(a)

straight alpha over straight beta plus straight beta over straight alpha

(b)

space space straight alpha squared plus straight beta squared

152 Views

Short Answer Type

424.

If α and β are the zeroes of the quadratic polynomial ax² + bx + c. Find the value of α²– β².

145 Views

425. If α and β are the zeroes of the quadratic polynomial ax² + bx + c, then find the value of α³ + β³.

129 Views

Long Answer Type

426. If α and β are the zeroes of quadratic polynomial ax² + bx + c, then find

straight alpha squared over straight beta plus straight beta squared over straight alpha.

134 Views

427. If α and β are the zeroes of the quadratic polynomial P(x) = Kx² + 4x + 4 such that α² + β² = 24, find the value of K.

433 Views

Short Answer Type

428. If α and β are the zeroes of quadratic polynomial x² + x – 2. Find the value of (α^–1 + β^–1).

107 Views

429. Find a quadratic polynomial when the sum and product of its zeroes respectively
(i)

space 1 fourth comma space minus 1

(ii)

square root of 2 comma space fraction numerator negative 1 over denominator 3 end fraction

152 Views

Long Answer Type

430. If α, β are the zeroes of the quadratic polynomial 2x²– 3x – 5, form a polynomial whose zeroes are 2α + 1 and 2β + 1.

Since, α, β are the zeroes of the quadratic polynomial 2x² – 3x – 5, then

straight alpha plus straight beta equals fraction numerator negative straight b over denominator straight a end fraction equals 3 over 2 space and space straight alpha. straight beta equals straight c over straight a equals fraction numerator negative 5 over denominator 2 end fraction

Now,

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Product space left parenthesis straight alpha. space straight beta right parenthesis space equals space left parenthesis 2 straight alpha plus 1 right parenthesis space left parenthesis 2 straight beta plus 1 right parenthesis space space space space space space space space space space space space space space space space space space space space space space space space space equals space 4 αβ plus 2 straight alpha plus 2 straight beta plus 1 space space space space space space space space space space space space space space space space space space space space space space space space space equals 4 αβ plus 2 left parenthesis straight alpha plus straight beta right parenthesis plus 1

equals 4 open parentheses fraction numerator negative 5 over denominator 2 end fraction close parentheses plus 2 open parentheses 3 over 2 close parentheses plus 1 space equals space minus 10 plus 3 plus 1 space equals space minus 6

So, required quadratic polynomial be K {x² –(α + β)x + α . β}= K {x²–5x –x 6}.

213 Views

Previous Year Papers

Test Series

Test Yourself

Long Answer Type

Short Answer Type

Long Answer Type

Short Answer Type

Long Answer Type

430. If α, β are the zeroes of the quadratic polynomial 2x2– 3x – 5, form a polynomial whose zeroes are 2α + 1 and 2β + 1.

430. If α, β are the zeroes of the quadratic polynomial 2x²– 3x – 5, form a polynomial whose zeroes are 2α + 1 and 2β + 1.