1.

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)).`


Discussion

No Comment Found