Solving a quadratic equation by formula method — lesson. Mathematics State Board, Class 10.

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The formula for finding the roots of the quadratic equation

$ax^2 + bx + c = 0$ is:

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

This formula is known as the quadratic formula.

Example:

Find the roots of

$2x^2 + 3x - 77 = 0$ by using quadratic formula.

Solution:

The given equation is

$2x^2 + 3x - 77 = 0$ .

Here,

$a = 2$ ,

$b = 3$ and

$c = -77$ .

Quadratic formula:

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

Substitute the given values in the formula.

$x = \frac{- 3 \pm \sqrt{3^{2} - 4 \times 2 \times (- 77)}}{2 \times 2}$

$x = \frac{- 3 \pm \sqrt{9 + 616}}{4}$

$x = \frac{- 3 \pm \sqrt{625}}{4}$

$x = \frac{- 3 \pm 25}{4}$

$x = \frac{- 3 + 25}{4}$ or

$x = \frac{- 3 - 25}{4}$

$x = \frac{22}{4}$ or

$x = \frac{- 28}{4}$

$x =$

$\frac{11}{2}$ or

$x = -7$

Therefore, the roots of the given equation are

$-7$ and

$\frac{11}{2}$ .

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7. Solving a quadratic equation by formula method