Question

If the product of zeros of the polynomial f(x) ax³ − 6x² + 11x − 6 is 4, then a =

Options

• \[\frac{3}{2}\]

• \[- \frac{3}{2}\]

• \[\frac{2}{3}\]

• \[- \frac{2}{3}\]

• \[- \frac{2}{3}\]

Answer 1

Since `alpha` and`beta` are the zeros of quadratic polynomial f(x) ax³ − 6x² + 11x − 6

`alpha + ß = - (text{coefficient of x})/(text{coefficient of } x^2)`

So we have 

`4 = ((-6)/a)`

`4 = 6/a`

`4a=6`

`a = 6/4`

`a= (3xxcancel(2))/(2xxcancel(2))`

`a = 3/2`

The value of a is `3/2`

Hence, the correct alternative is (a).