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Question

If the product of zeros of the polynomial $$2x^2-6x-(6-a)$$ is $$4$$, then find a.


A
2
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B
10
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C
16
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D
14
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Solution

The correct option is B $$14$$
$$\Rightarrow$$  The given quadratic equation is $$2x^2-6x-(6-a)$$, comparing it with $$Ax^2+Bx+C=0$$
$$\Rightarrow$$  We get, $$A=2,\,B=-6,\,C=-(6-a)$$
$$\Rightarrow$$  Product of the zeros $$=4$$
$$\Rightarrow$$  $$\dfrac{C}{A}=4$$
$$\Rightarrow$$  $$\dfrac{-(6-a)}{2}=4$$
$$\Rightarrow$$  $$-6+a=8$$
$$\Rightarrow$$  $$a=8+6$$
$$\therefore$$  $$a=14$$

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