If $x = 2 / 3$ and $x = - 3$ are the roots of the equation $a x^{2} + 7 x + b = 0$ , find the values of $a$ and $b$ .

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Solution

If $x = \frac{2}{3}, x = - 3$ are roots of the equation $a x^{2} + 7 x + b = 0$ then

$(x - \frac{2}{3}) (x - (- 3)) = 0$

$\Rightarrow (x - \frac{2}{3}) (x + 3) = 0$
$\Rightarrow x^{2} - \frac{2}{3} x + 3 x - 2 = 0$

$\Rightarrow x^{2} + \frac{7}{3} x - 2 = 0$

$\Rightarrow 3 x ² + 7 x - 6 = 0$

Compare the equation with $a x ² + 7 x + b = 0$

Therefore, $a = 3, b = - 6$

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Similar questions

If $x = \frac{2}{3}$ and x = - 3 are the roots of equation $a x^{2} + 7 x + b = 0,$ find values of a and b.

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