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

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

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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

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424.

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

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

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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.

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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.

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

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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

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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.

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