Question

What is the zero in the quadratic function f(x)= 9x^2-54x-19?

Answer 1

Answer:

6.33... and 0.333...

Step-by-step explanation:

The quadratic formula is

$x=\frac{-b+\sqrt{b^2-4ac} }{2a}$.

It is important because while some quadratics are factorable and can be solved not all are. The formula will solve all quadratic equations and can also give both real and imaginary solutions.  Using the formula will require less work than finding the factors if factorable. We will substitute a=9, b=-54 and c=-19.

$x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}\\x=\frac{-(-54)+/-\sqrt{(-54)^2-4(9)(-19)} }{2(9)}\\x=\frac{54+/-\sqrt{2916+684} }{18}$

We will now solve for the plus and the minus.

The plus,,,

$x=\frac{54+\sqrt{3600}}{18}\\x=\frac{54+60}{18}\\x=\frac{114}{18}\\x=6.3$

and the minus...

$x=\frac{54-\sqrt{3600}}{18}\\x=\frac{54-60}{18}\\x=\frac{-6}{18}\\x=-0.333...$