Question

Is the following quadratic polynomial reducible or irreducible?
$f\left(x\right)=-2x^2-2x-1$

• A. Reducible with one real root
• B. Reducible with two real roots
• C. Irreducible
• D. None of these

Answer 1

Answer: (C)

Irreducible

To check whether the given quadratic polynomial is reducible or irreducible, we need to calculate the discriminant

Calculate the discriminant for the equation, $-2x^2-2x-1=0$

$D=b^2-4ac=(-2{)}^2-4(-2\left)\right(-1)=-4<0$

Quadratic equation is irreducible if $D<0$

$\therefore$ The quadratic polynomial is irreducible.

Correct option is C