> Solution Product of 3 zeros of a cubic polynomial = -d/a Let the third zero be k Product of 2 zeros = 3 So, -d/a = 3k -9/2=3k k= -3/2 0 Let αβγ be the zeros of polynomial f(x) = 2x3 + 6x2 − 4x + 9 such that `alphabeta=3` We have, `alpha ß y= - (text{coefficient of x})/(text{coefficient of } x^2)` `=(-9)/2` Putting `alphabeta` in `alpha beta y`, we get `alpha beta y = (-9)/2` `3 y = (-9)/2xx1/3` `y = (-3)/2` Therefore, the value of third zero is `(-3)/2`
Hence, the correct alternative is (b). |