Question

find integral zeros of the polynomial​

Answer 1

Answer:

There is only one integral zero, which is x=1

Step-by-step explanation:

we are given a polynomial. We have to find its zeros. So, we equate the polynomial to zero.

2x^3+5x^2-5x-2=0

Here, Sum of all coefficients of the polynomial is zero. This means that (x-1) is a factor.

2x^3+5x^2-5x-2=0 \\ \\ \implies 2x^3-2x^2 + 7x^2-7x +2x -2=0 \\ \\ \implies 2x^2(x-1)+7x(x-1) + 2(x-1)=0 \\ \\ \implies (x-1)(2x^2+7x+2)=0 \\ \\ \implies \boxed{x=1} \, \, \,OR \, \, \, 2x^2+7x+2=0

Now, 2x^2+7x+2=0  is a quadratic equation.

Its Discriminant is:

D=b^2-4ac =7^2 - 4(2)(2) = 33

Since D is not a perfect square, the roots are irrational. Thus, two zeros of original polynomial are irrational.