1.

Find a quadratic polynomial whose zeros are 1 and `-3`. Verify the relation between the coefficients and zeros of the polynomial.

Answer» Let `alpha = 1 and beta =- 3.`
Sum of zeros = `(alpha+beta) = 1 +(-3)=-2.`
Product of zeros = `alpha beta = 1 xx (-3) =- 3.`
So, the required polynomial is
`x^(2)-(alpha+ beta) x+alpha beta = x^(2) -(-2) x+(-3)`
` = x^(2) + 2x -3.`
Sum of zeros `=-2=(-2)/1 =(-("coefficient of x"))/(("coefficient of " x^(2))),`
product of zeros `=- 3=(-3)/1 = ("constant term")/("coefficient of " x^(2)).`


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