Review question

# Can we find the coefficients and factorise this quartic? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R9330

## Question

The expression $2x^4+ax^3+bx^2-4x-4$ where $a$ and $b$ are constants, is denoted by $f(x)$. Given that $f\left(-\dfrac{1}{2}\right)=0$ and $f(2)=0$, find the values of $a$ and $b$.

With these values for $a$ and $b$

1. express $f(x)$ as the product of three algebraic factors, and hence show that the equation $f(x)=0$ has only two real roots;

2. find the set of values of $x$ for which $f(x)>0$.