## 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

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)

## Online Coaching Course for CAT Exam Preparation

a) 750+ Videos covering entire CAT syllabus
b) 2 Live Classes (online) every week for doubt clarification
c) Study Material & PDFs for practice and understanding
d) 10 Mock Tests in the latest pattern
e) Previous Year Questions solved on video

## Question

If x + 1 = x^2 and x > 0, then 2x^4 is

A) 6 + 4√5
B) 3 + 5√5
C) 5 + 3√5
D) 7 + 3√5

Option (D)

## Solution

As per CAT 2017 – Quantitative Aptitude – Algebra – Quadratic Equation, we can see that
x+1=x^2
Find out the roots of x = [1+/- root(5)]/2
X2 = [3 +/- √5]/2
X4 = [7 +/-3√5]/2
2×4 = 7 +/- 3√5
As the only option is 7 + 3√5 So, we go with that.
Option (D)

## CAT 2017 Questions from Quantitative Aptitude – Algebra

Quantitative Aptitude – Algebra – Quadratic Equations – Ques: 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
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

## Online Coaching Course for CAT Exam Preparation

a) 750+ Videos covering entire CAT syllabus
b) 2 Live Classes (online) every week for doubt clarification
c) Study Material & PDFs for practice and understanding
d) 10 Mock Tests in the latest pattern
e) Previous Year Questions solved on video