Question

Show that 3 is a zero of the polynomial 2x3-x2-13x-6.hence find all the zeros of this polynomial

Answer 1

Hello,

P(x) = 2x³-x²-13x-6
Given
3 is a zero of polynomial p(x)

So
By factor theorem

(x - 3) is a factor of p (x)

Now
On dividing


$(2 {x}^{3} - {x}^{2} - 13x - 6) \div (x - 3)$
We get the answer as
2x²+5x+2

factorization of this polynomial
2x²+4x+x+2
2x(x+2)+1(x+2)
(x+2)(2x+1)

So,

P(x) = (x-3) (2x²+5x+2)
P(x) = (x-3)(x+2)(2x+1)

So ,
The Zeroes of the polynomial are

3, (-2) and (-1)/2


Hope this will be helping you ✌️

Answer 2

hey....here is your answer in the attachment