1.

Find the zeros of the polynomial `2x^(2)+5x-12` and verify the relationship between its zeros and coefficients.

Answer» Let the given polynomial be denoted by f(x). Then,
`f(x) = 2x^(2)+5x-12`
` = 2x^(2) + 8x - 3x - 12`
` =2x(x+4) - 3(x+4)`
` = (x+4)(2x-3)`.
`:. F(x) = 0 rArr (x+4)(2x-3) = 0`
` rArr x+4 = 0 or 2x - 3 = 0`
` rArr x =- 4 or x = 3/2.`
So, the zeros of f(x) are `-4 and 3/2.`
Sum of the zeros = `(-4+3/2)=(-5)/2 = (-("coefficient of x"))/(("coefficient of " x^(2))),`
product of the zeros = `(-4) xx 3/2 = (-12)/2 = ("constant term")/(("coefficient of " x^(2))).`


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