Question

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

Answer 1

Step-by-step 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)=(-b\pm√(b^2-4ac))/(2a)`
`\mathrm{For\: }\quad a=1,\: b=-5,\: c=-14`
`x_(1,2)=(-\left(-5\right)\pm√(\left(-5\right)^2-4\cdot\:1\cdot\left(-14\right)))/(2\cdot\:1)`

Multiplying numbers:

`x_(1,2)=(-(-5)\pm√(5^2+56))/(2)`

Computing the power and adding numbers:

`x_(1,\: 2)=(-(-5)\pm√(81))/(2)`

Simplifying:

`x_(1,\: 2)=(-(-5)\pm9)/(2)`

Separate the solutions:

`x_1=(5+9)/(2),\: x_2=(5-9)/(2)`

Simplifying:

`x_1=(14)/(2),\: x_2=(-4)/(2)`

Simplifying again the expression:

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

The zeros of the function are:

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