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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.

Since, α and β are the zeroes of the quadratic polynomial P(x) Kx + 4x + 4, then

straight alpha plus straight beta equals fraction numerator negative straight b over denominator straight a end fraction equals fraction numerator negative 4 over denominator straight K end fraction space and space straight alpha comma space straight beta space equals space straight c over straight a equals 4 over straight K

It is given that

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rightwards double arrow

space space space space left parenthesis straight alpha plus straight beta right parenthesis squared minus 2 αβ space equals space 24

rightwards double arrow

open parentheses fraction numerator negative 4 over denominator straight K end fraction close parentheses squared minus 2 open parentheses 4 over straight K close parentheses space equals space 24

rightwards double arrow

16 over straight K squared minus 8 over straight K equals 24

rightwards double arrow

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rightwards double arrow

16 minus 8 straight K space equals space 24 space straight K squared

rightwards double arrow

24 space straight K squared plus 8 straight K minus 16 space equals 0

rightwards double arrow space space space 8 left parenthesis 3 straight K squared plus straight K minus 2 right parenthesis space equals space 0

space space space rightwards double arrow space space space space space space space space space space space space space space 3 straight K squared plus straight K minus 2 equals 0

rightwards double arrow

3 straight K squared plus 3 straight K minus 2 straight K plus 2

rightwards double arrow

3 straight K left parenthesis straight K plus 1 right parenthesis minus 2 left parenthesis straight K plus 1 right parenthesis space equals space 0

rightwards double arrow

space space space space left parenthesis 3 straight K minus 2 right parenthesis space left parenthesis straight K plus 1 right parenthesis space equals space 0

rightwards double arrow

space 3 straight K minus 2 equals 0 space space or space space straight K plus 1 equals 0

rightwards double arrow

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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.

213 Views

Previous Year Papers

Test Series

Test Yourself

Long Answer Type

Short Answer Type

Long Answer Type

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.

Short Answer Type

Long Answer Type

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.