Question

Find all the zeros of polynomial 4x⁴-20x³+23x²+5x-6, if two of its zeros are 2 and 3.

Answer 1

Answer:

2,3,1/2,-1/2

Step-by-step explanation:

Given, 2 and 3 are the zeroes of the polynomial p(x).

So, (x - 2) (x - 3) are factors of the polynomial p(x).

Thus, (x2 - 5x + 6) is a factor of the polynomial p(x).

We have:

4x4 - 20x3 + 23x2 + 5x - 6 = (x2 - 5x + 6) (4x2 - 1)

= (x - 2) (x - 3) (2x - 1) (2x + 1)

Therefore, 2, 3, are the zeroes of p(x)