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
B
2ac=b(a+b)
C
a2+b2=c2
D
a2+b2=a+b

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.Maths

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