For what integer values of 'm' the roots of the equation $x^{2} - 2 x (1 + 3 m) + 7 (3 + 2 m) = 0$ will be equal?

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Solution

Roots are equal when
$D = b^{2} - 4 a c = 0 \Rightarrow 4 {(1 + 3 m)}^{2} - 4.7 (3 + 2 m) = 0 \Rightarrow 1 + 9 m^{2} + 6 m - 21 - 14 m = 0 \Rightarrow 9 m^{2} - 8 m - 20$
$\Rightarrow m = - \frac{10}{9}$ or $m = 2$

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