Question

Solve using the quadratic formula. Show all work. Write each solution in simplest form. No decimals.

Answer 1

Given:

The quadratic equation is:

$12a^2+9a+7=0$

To find:

The solution of the given equation in simplest form by using the quadratic formula.

Solution:

If a quadratic equation is $ax^2+bx+c=0$, then the quadratic formula is:

$x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}$

We have,

$12a^2+9a+7=0$

Here, $a=12,b=9,c=7$. Using the quadratic formula, we get

$x=\dfrac{-(9)\pm \sqrt{(9)^2-4(12)(7)}}{2(12)}$

$x=\dfrac{-9\pm \sqrt{81-336}}{24}$

$x=\dfrac{-9\pm \sqrt{-255}}{24}$

$x=\dfrac{-9\pm i\sqrt{255}}{24}$              $[\because \sqrt{-a}=i\sqrt{a}]$

The solutions of the given equations are $x=\dfrac{-9-i\sqrt{255}}{24}$ and $x=\dfrac{-9+i\sqrt{255}}{24}$.

Therefore, the correct option is B.