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P(x) = x2 + 2x + 1 find the sum of products of the zeroes and verify relationship to the coefficients of terms in the polynomial. |
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Answer» \(P(x) = x^2 + 2x + 1\) \(P(x) = 0\) gives \(x^2 + 2x + 1 = 0\) ⇒ \((x + 1)^2 = 0\) ⇒ \(x + 1 = 0 \,or\, x + 1 = 0\) \(x = -1 \,or\,x = -1\). Sum of zeros = \(-1 - 1 = -2 = \frac{-2}1 = \frac{-b}a = \frac{\text{-coefficient of }x}{\text{coefficient of }x^2}\) Product of zeros = \((-1)(-1) = 1 = \frac11 = \frac ca = \frac{\text{constant term}}{\text{coefficient of }x^2}\) |
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