Quadratic formula

What is the quadratic formula?

The quadratic formula is a formula that helps us to find the solutions of an equation of degree 2. First of all, we need to turn our equation of degree 2 to standard form $ax^2+bx+c=0$.

The quadratic formula is: $\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}$.

How to use the quadratic formula?

Let’s see some examples of the quadratic formula.

Example 1: Solve the quadratic equation $x^2+5x+6=0$.
Solution: In this quadratic equation a=1, b=5 and c=6. We put these numbers into the quadratic formula and we get:
$\dfrac{-5\pm \sqrt{25-24}}{2}=\dfrac{-5 \pm 1}{2}=-2,-3$.

Example 2: Solve the quadratic equation $x^2+5x+7=0$.
Solution: In this quadratic equation a=1, b=5 and c=7. We put these numbers into the quadratic formula and we get:
$\dfrac{-5\pm \sqrt{25-28}}{2}=$. As you see, under the square root we have a negative number, so there we have no solution for this quadratic equation.

When do we use the quadratic formula?

The quadratic formula is the most general formula to find solutions to quadratic equations. You can use it when you have a quadratic equation.

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