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Quantitative Aptitude :: Square Root and Cube Root - Discussion

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Choose the correct option.

The minimum possible value of the sum of the squares of the roots of the equation x^2 + (a+3)x - (a-5) = 0 is

A1

B2

C3

D4

Answer: Option (Login/Signup)

Show Explanation

x+y=-(a+3)

x*y=-(a+5)

now, x^2 + y^2 = (x+y)^2 - 2x*y

                        = a^2 + 9 + 6a + 2a + 10

                        = a^2 + 8a + 19 = (a+4)^2 +3


the minimum value of this could be when (a+4)^2=0 at a=-4

therefore, minimum value is 3.

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