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

Quantitative Aptitude – Algebra – Quadratic Equations

Question

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)

Download CAT 2017 Question Paper with answers and detailed solutions in PDF

CAT 2017 Questions from Quantitative Aptitude – Algebra

Quantitative Aptitude – Algebra – Quadratic Equations – Ques: If x + 1 = x^2 and x > 0, then 2x^4 is
Quantitative Aptitude – Algebra – Functions
Quantitative Aptitude – Algebra – Logarithms
Quantitative Aptitude – Algebra – Maxima Minima
Quantitative Aptitude – Algebra – Inequalities
Quantitative Aptitude – Algebra – Polynomials
Quantitative Aptitude – Algebra – Simple Equations

Other posts related to Quantitative Aptitude – Algebra

Problems on Ages with complete solutions, answers, and tricks to solve
How to Solve Number of Integral Solutions Questions for CAT 2017
Quadratic Equations
Basic Functions and Modifications of Graphs
An introduction to functions (Algebra) for CAT 2017 exam
Functions from Algebra – Basic concepts and application for Quantitative Aptitude in CAT Exam