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Question

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


Solution

According to given data,
$$\left(x-\cfrac{2}{3}\right)(x+3)=0$$
$$\implies x^2+3x-\cfrac{2x}{3}-2=0$$
$$\implies x^2+\cfrac{7x}{3}-2=0$$
$$\implies 3x^2+7x-6=0$$

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

Mathematics
RS Agarwal
Standard IX

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