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Polynomials

Short Answer Type

481. Find a quadratic polynomial whose sum of zeroes and product of zeroes are given below:

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

303 Views

Long Answer Type

482. If α. β are the zeroes of the quadratic polynomial x²–x – 2, form an equation whose zeroes are (2a + 1) and (2p + 1).

87 Views

483. If α and β are the zeroes of the quadratic polynomial 2x² – 5x + 7, form an equation whose zeroes are (2α + 3β) and (3α + 2β).

93 Views

484. If α, β are the zeroes of the quadratic polynomial 2x² – 3x + 1, form an equation whose zeroes are

straight alpha over straight beta space and space straight beta over straight alpha.

112 Views

485. It being given that 1 is one of the zeroes of the polynomial f(x) = 7x – x³ – 6 find its other zeroes.

160 Views

Short Answer Type

486. Divide (3x³ – 4x² + 7x – 2) by (2 – x + x²) and verify the division algorithm.

181 Views

Long Answer Type

487. Find all the zeroes of the polynomial 2x⁴ – 10x³ + 5x² + 15x – 12, if its zeroes are;

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415 Views

Short Answer Type

488. Find all the zeroes of the polynomial x³ + 3x² – 4x – 12, if one of its zeroes is –3.

Solution not provided.
Ans. $plus-or-minus 2$

115 Views

489. On dividing the polynomial 4x⁴ – 5x³ – 39x² – 46x – 2 by the polynomial g(x). the quotient is x² – 3x x - 5 and the remainder is –5x + 8. Find the polynomial g(x).

246 Views

490. Apply the division algorithm to find the quotient and the remainder in division of p(x) by g(x) as given below:
p(x) = x² + 11x + 25, g(x) = x + 6.

100 Views