Question

Determine the number of zeros of the function,
4) y = 2x² + 12x + 17

Answer 1

Explanation:

The zeroes of a function are those values that touches the x-axis. In order to find those values we must set $y=0$:

$0=2x^2+12x+17 \\ \\ \text{Using quadratic formula}: \\ \\ x=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \\ \\ \\ a=2 \\ \\ b=12 \\ \\ c=17 \\ \\ \\ x=\frac{-12 \pm \sqrt{12^2-4(2)(17)}}{2(2)} \\ \\ x=\frac{-12 \pm \sqrt{8}}{4} \\ \\ x=\frac{-12 \pm 2\sqrt{2}}{4} \\ \\ \\ \text{Two values}: \\ \\ x_{1}=\frac{-6 + \sqrt{2}}{2} \\ \\ x_{2}=\frac{-6 - \sqrt{2}}{2}$

Finally, there are two zeros of the function that are:

$\boxed{x_{1}=\frac{-6 + \sqrt{2}}{2}} \\ \\ \\ \boxed{x_{2}=\frac{-6 - \sqrt{2}}{2}}$