$2 x (3 x + 5) + 3 (3 x + 5) = a x^{2} + b x + c$
In the equation above, a, b, and c are constants. If the equation is true for all values of $x$ , what is the value of $b$ ?

19

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12

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25

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9

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Solution

The correct option is B $19$
Given $2 x (3 x + 5) + 3 (3 x + 5) = a x^{2} + b x + c$
$\Rightarrow 6 x^{2} + 10 x + 9 x + 15 = a x^{2} + b x + c$
$\Rightarrow 6 x^{2} + 19 x + 15 = a x^{2} + b x + c$
Now comparing cofficients of x. we get,
$19 = b$
$∴ b = 19$

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