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Question

If one root of $$x^{2}+ax+8=0$$ is $$4$$ and the equation $$x^{2}+ax+b=0$$ has equal roots, then $$b=$$


A
7
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B
9
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C
1
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D
3
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Solution

The correct option is A $$9$$
$$x^2+ax+8=0$$ has one of it roots as $$4$$
$$\Rightarrow 4^2+4a+8=0$$
$$\Rightarrow 4\left[ 4+a+2\right]=0$$
$$\Rightarrow 6+a=0$$
$$\Rightarrow a=-6$$
Now, the equation 
$$\Rightarrow x^2+ax+b=0$$
     $$x^2-6x+b=0$$
has double ( equal ) roots.
In a quadratic equation, the roots will be equal if and only if the discrimination (D)=0
Now, the discriminant of the above quadratic equation is 
$$\Rightarrow D=B^2-4AC=0$$
$$\Rightarrow 6^2-4\cdot 1 \cdot b=0$$
$$\Rightarrow 6^2=4b$$
$$\Rightarrow b=\dfrac{36}{4}=9$$
$$\therefore a=-6$$  and   $$b=9$$
Hence, the answer is $$9.$$


Mathematics

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