Quantitative Aptitude :: Square Root and Cube Root - Discussion
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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
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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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STEP-BY-STEP
let x and y be the two roots of the equation.
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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