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Question

If sum of the roots of the equation $$ax^2 + bx + c = 0$$ is equal to the sum of their squares, then


A
2ac=ab+c
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B
2ac=b(a+b)
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C
a2+b2=c2
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D
a2+b2=a+b
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Solution

The correct option is A $$2ac = b(a + b)$$
Sum of the roots of the equation $$ax^2 + bx + c = 0$$ is equal to the sum of their squares.
Let $$\alpha,\beta$$ be the roots.
$$\Rightarrow\displaystyle \alpha+\beta=\dfrac{-b}{a}$$ and $$\alpha\beta=\displaystyle\dfrac{c}{a}$$
$$\alpha+\beta=\alpha^2+\beta^2$$
$$\displaystyle\dfrac{-b}{a}=\left(\dfrac{-b}{a}\right)^2-2\left(\dfrac{c}{a}\right)$$
          $$=\displaystyle\dfrac{b^2-2ac}{a^2}$$
$$\Rightarrow -ab=b^2-2ac$$
$$\therefore  2ac=b(a+b)$$
Hence, option B.

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