Question

Find the zewo of the polynomial
P(x) =(x-4) ² (16)​

Answer 1

ANSWER

p(x)=x

3

−5x

2

−16x+80

Let α,β,γ are the zeroes of polynomial p(x) such that α+β=0.

Then,

Sum of zeros = −

Coefficient of x

3

Coefficient of x

2

α+β+γ=5

0+γ=5

γ=5

Also,

Product of zeros = −

Coefficient of x

3

Constant term

αβγ=−80

−5α

2

=−80

α

2

=16

α=±4

Now,

α+β=0

⟹±4+β=0

β=∓4

Thus, zeros of the given polynomial are 4,−4,5.