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351. Verify that the numbers given alongside of the cubic polynomials below are their zeroes. Also, verify the relationship between the zeroes and coefficients in each case:
x³ - 4x² + 5x - 2; 2, 1, 1

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Short Answer Type

352. Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes as 2, -7, -14 respectively.

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Long Answer Type

353. If the zeroes of the polynomial x³ – 3x²+ x + 1 are (a – b), a, (a + b), find a and b.

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354. If two zeroes of the polynomial x⁴ – 26x³-26x² + 138x –35 are 2 ±

square root of 3

, find other two zeroes.

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355. If the polynomial x⁴ – 6x³ + 16x² – 25x + 10 is divided by another polynomial x² - 2x + k, the remainder comes out to be x + a, find ‘k’ and ‘a’.

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Short Answer Type

356. Is x = 1 a zero of polynomial x³– a² – x + 1 ?

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At $straight x equals 1 comma$ the value of p(x) is
$straight P left parenthesis 1 right parenthesis space equals space 1 cubed minus 1 squared minus 1 plus 1 space space space space space space space space space equals space 1 minus 1 minus 1 plus 1 space space space space space space space space space equals space 2 space minus 2 space equals 0$
Hence, x = 1 is a zero of polynomial x³ – a² - x + 1.