# If the roots of 2x^2+4x-1=0 are a and b, find a^2+b^2?

Dec 11, 2016

${a}^{2} + {b}^{2} = 5$

#### Explanation:

Sum of roots in a qudratic equation $p {x}^{2} + q x + r = 0$ is $- \frac{q}{p}$ and product of roots is given by $\frac{r}{p}$.

If roots of $2 {x}^{2} + 4 x - 1 = 0$ are $a$ and $b$, we have

we have $\left(a + b\right) = - \frac{4}{2} = - 2$ and

$a b = - \frac{1}{2}$

Hence ${a}^{2} + {b}^{2} = {a}^{2} + 2 a b + {b}^{2} - 2 a b$

= ${\left(a + b\right)}^{2} - 2 a b$

= (-2)^2-2×(-1/2)

= $4 + 1$

= $5$