If the product of two zeros of the polynomial p(x 2x³ 6x² 4x + 9 is 3, then find its third zero)

>

If product of the two zeroes of the polynomial p x =2 x 3++6 x 2 4 x +9 is 3 , then find its third zero

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

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).