Question 1

What is the quadratic formula?

Accepted Answer

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

The quadratic formula is an equation used to solve 2nd order polynomial equations of the form $ax^2+bx+c=0$. It will find the value(s) of $x$ for given constants a, b, and c.

Question 2

How to solve quadratic formula?

Accepted Answer

Let's look at an example:

$2x^2-3x-5=0$

In this case $a=2$, $b=-3$, and $c=-5$ (don't forget the minus signs, this is a common mistake).

We now substitute these values into the quadratic equation:

$x=\frac{-(-3)\pm\sqrt{(-3)^2-4(2)(-5)}}{2(2)}$

Simplifying we get

$x=\frac{(3)\pm\sqrt{9+40}}{4}$

$x=\frac{3\pm\sqrt{49}}{4}$

$x=\frac{3\pm7}{4}$

The $\pm$ sign implies that we have two solutions for x. For the first solution you take the plus sign, for the second you take the minus sign to get

$x_1$=$\frac{3+7}{4}=\frac{5}{2}$

and

$x_2$=$\frac{3-7}{4}=-1$

The values $\frac{5}{2}$ and -1 solve the equation $2x^2-3x-5=0$.

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