Question

obtain all other zeros of x cube minus 3 x square - 6 X + 8, if one of its zero is 4​

Answer 1

To find :

We have to find the other zeroes of the polynomial (x³ - 3x² - 6x + 8) where it's one zero is 4.

Solution :

Since 4 is a zero, we have a factor (x - 4) of the given polynomial

Now, x³ - 3x² - 6x + 8

= x³ - 4x² + x² - 4x - 2x + 8

= x² (x - 4) + x (x - 4) - 2 (x - 4)

= (x - 4) (x² + x - 2)

= (x - 4) (x² + 2x - x - 2)

= (x - 4) {x (x + 2) - 1 (x + 2)}

= (x - 4) (x + 2) (x - 1)

So, we get other two factors (x + 2) and (x - 1) for the given trinomial.

∴ the other two zeroes are (- 2) and 1