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Find the zeros of the polynomial `f(x)=x^(2)-2` and verify the relationship between its zeros and coefficients. |
Answer» We have `f(x)= (x^(2)-2)={x^(2)-(sqrt2)^(2)} = (x+sqrt2)(x-sqrt2).` ` :. F(x) = 0 rArr (x+sqrt2)(x-sqrt2)= 0` ` rArr x +sqrt2 = 0 or x -sqrt2 = 0` ` rArr x =- sqrt2 or x = sqrt2.` So, the zeros of f(x) are ` -sqrt2 and sqrt2.` Sum of zeros = `(-sqrt2+sqrt2) =0 = 0/1 = (-"(coefficient of x)")/(("coefficient of " x^(2))), ` Product of zeros = `(-sqrt2) xx (sqrt2) = (-2)/1 = ("constant term")/("coefficient of " x^(2)).` |
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