Question

- Polynomial Functions - Find the zeros of each function algrebraically. If there is no real zero, state so.

Answer 1

EXPLANATION

Given the function f(x) = x^2 -5x - 14

$\mathrm{For\: a\: quadratic\: equation\: of\: the\: form\: }ax^2+bx+c=0\mathrm{\: the\: solutions\: are\: }$$x_{1,\: 2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$\mathrm{For\: }\quad a=1,\: b=-5,\: c=-14$$x_{1,2}=\frac{-\left(-5\right)\pm\sqrt{\left(-5\right)^2-4\cdot\:1\cdot\left(-14\right)}}{2\cdot\:1}$

Multiplying numbers:

$x_{1,2}=\frac{-(-5)\pm\sqrt{5^2+56}}{2}$

Computing the power and adding numbers:

$x_{1,\: 2}=\frac{-(-5)\pm\sqrt{81}}{2}$

Simplifying:

$x_{1,\: 2}=\frac{-(-5)\pm9}{2}$

Separate the solutions:

$x_1=\frac{5+9}{2},\: x_2=\frac{5-9}{2}$

Simplifying:

$x_1=\frac{14}{2},\: x_2=\frac{-4}{2}$

Simplifying again the expression:

$x=7,\: x=-2$

The zeros of the function are:

$(7,0),\text{ (-2,0)}$