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}

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

x = \frac{22}{4}

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