Solve : m² - 14 m + 13 = 0 - Vidyadip

Question

Solve : m² - 14 m + 13 = 0

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Answer

$\begin{array}{l}m^2-14 m+13=0 \text { comparing } \\ \text { with } a x^2+b x+c=0 \\ \text { we get } a=1, b=-14, c=13, \\ \therefore b^2-4 a c=(-14)^2-4 \times 1 \times 13 \\ =196-52 \\ =144 \\ \qquad \begin{array}{l} m=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a} \\ = \frac{-(-14) \pm \sqrt{144}}{2 \times 1} \\ =\frac{14 \pm 12}{2}\end{array}\end{array}$
$\therefore m=\frac{14+12}{2}$ or $m=\frac{14-12}{2}$
$\therefore m=\frac{26}{2}$ or $m=\frac{2}{2}$
$\therefore m=13$ or $m=1$
$\therefore 13$ and 1 are roots of the equation.

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