What is an example of the Quadratic Formula?

For the equation $x^2 - 5x + 6 = 0$, with $a=1$, $b=-5$, $c=6$, the formula yields $x = \frac{-(-5) \pm \sqrt{(-5)^2 - 4(1)(6)}}{2(1)} = \frac{5 \pm \sqrt{25 - 24}}{2} = \frac{5 \pm 1}{2}$, giving roots $x=3$ and $x=2$.

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Q: What should I remember about the Quadratic Formula?

The expression $b^2 - 4ac$ within the formula is known as the discriminant, which determines the number and type of roots (real or complex). This formula is universally applicable for solving any quadratic equation, regardless of whether its roots are rational, irrational, or complex.

The rule

Description

The quadratic formula provides the solutions, also known as roots, for any quadratic equation of the form $a x^{2} + b x + c = 0$ , where $a \neq = 0$ . It expresses the variable $x$ in terms of the coefficients $a$ , $b$ , and $c$ .

See it in action

Examples

1

For the equation $x^{2} - 5 x + 6 = 0$ , with $a = 1$ , $b = - 5$ , $c = 6$ , the formula yields $x = \frac{- ( - 5 ) \pm ( - 5 ) ^{2} - 4 ( 1 ) ( 6 )}{2 ( 1 )} = \frac{5 \pm 25 - 24}{2} = \frac{5 \pm 1}{2}$ , giving roots $x = 3$ and $x = 2$ .

Good to know

Key Facts

The expression $b^{2} - 4 a c$ within the formula is known as the discriminant, which determines the number and type of roots (real or complex).
This formula is universally applicable for solving any quadratic equation, regardless of whether its roots are rational, irrational, or complex.

Common questions

Frequently Asked Questions

The quadratic formula provides the solutions, also known as roots, for any quadratic equation of the form $a x^{2} + b x + c = 0$ , where $a \neq = 0$ . It expresses the variable $x$ in terms of the coefficients $a$ , $b$ , and $c$ .

For the equation $x^{2} - 5 x + 6 = 0$ , with $a = 1$ , $b = - 5$ , $c = 6$ , the formula yields $x = \frac{- ( - 5 ) \pm ( - 5 ) ^{2} - 4 ( 1 ) ( 6 )}{2 ( 1 )} = \frac{5 \pm 25 - 24}{2} = \frac{5 \pm 1}{2}$ , giving roots $x = 3$ and $x = 2$ .

The expression $b^{2} - 4 a c$ within the formula is known as the discriminant, which determines the number and type of roots (real or complex). This formula is universally applicable for solving any quadratic equation, regardless of whether its roots are rational, irrational, or complex.