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4. Obtain all other zeroes of the polynomial x-3/2x3+ 3x2 +3,2x-4, if two of its zeroes are2 and 22 |
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Answer» P(x) = x⁴ - 3 √2 x³ + 3 x² + 3√2 x - 4 given that (x - √2) , (x - 2√2) are factors of P(x) as √2 and 2√2 are two zeroes of P(x) = 0. (x -√2) (x - 2√2) = x² -3√2 x + 4 is a factor of P(x). let A be a constant. We can write the constant term in the second factor by : -4/4 = -1... dividing the constant terms. let (x² - 3√2 x + 4) (x² + A x -1 ) = P(x) Now compare the coefficients of x³ : A - 3√2 = -3√2 => A = 0 coefficient of x : 4A + 3√2 = 3√2 => A = 0 so the other factors are : x² - 1 = 0 so x = 1 and -1 are the other factors. This method of multiplying the factors and comparing coefficients is simple. |
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