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

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Solution

According to given data,
$(x - \frac{2}{3}) (x + 3) = 0$
$⟹ x^{2} + 3 x - \frac{2 x}{3} - 2 = 0$
$⟹ x^{2} + \frac{7 x}{3} - 2 = 0$
$⟹ 3 x^{2} + 7 x - 6 = 0$

By comparing with $a x^{2} + 7 x + b = 0$
We get, $b = - 6$ and $a = 3$

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

x = \frac{2}{3}

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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.

x = \frac{2}{3}

x = - 3

a x^{2} + 7 x + b = 0

a

b

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