Quantitative Aptitude – Algebra – Quadratic Equations – The minimum possible value


Quantitative Aptitude – Algebra – Quadratic Equations


Question


CAT 2017 - Afternoon slot - Quantitative Aptitude - Algebra - Quadratic Equations - The minimum possible value
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

A) 1
B) 2
C) 3
D) 4

Answer


Option (C)

Solution


From CAT 2017 – Quantitative Aptitude – Algebra – Quadratic Equations, we can see that,

b and c can be the roots of the given equation.
We have to find, b^2 + c^2 = (b+c)^2 – 2bc
b+c = -(a+3) and bc = -(a+5)
b^2 + c^2 = (a+3)^2 + 2(a+5) = a^2 + 8a + 19
Min value of a quadratic equation = -Discriminant (D)/4*First term
D = b^2 – 4ac = 64 – 76 = -12
Min value = 12/4 = 3
Option (C)

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