Question

Would like this problem broken down step by step thanks!

Answer 1

Answer:

m=12

Explanation:

Given any quadratic function, y=ax²+bx+c.

We can determine the nature of the roots of such quadratic function by examining the discriminant, D where:

$D=b^2-4ac$

• If D>0, the roots are real and unequal.

,

• If D=0, the roots are real and equal.

,

• If D<0, the roots are complex.

In our given equation:

$\begin{gathered} y=18x^2+mx+2 \\ a=18,b=m,c=2 \end{gathered}$

For the function to have exactly one zero, the value of D=0.

$\begin{gathered} D=b^2-4ac=m^2-4(18)(2)=m^2-144 \\ D=0\implies m^2-144=0 \\ Add\text{ 144 to both sides.} \\ m^2=144 \\ Take\text{ the square root of both sides} \\ \sqrt{m^2}=\sqrt{144} \\ m=12 \end{gathered}$

The value of m for which the function will have one zero is 12.