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 +
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Quantitative Aptitude - Algebra - Quadratic Equation - If x + 1 = x^2
Quantitative Aptitude - Algebra - Quadratic Equation
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
Answer
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
2x4 = 7 +/- 3√5
As the only option is 7 + 3√5 So, we go with that.
Option (D)
Down
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Quantitative Aptitude – Algebra - Quadratic Equations – If a and b are integers such that 2x^2
Slot -2 – Quantitative Aptitude – Algebra - Quadratic Equations – If a and b are integers such that 2x^2
If a and b are integers such that 2x^2 −ax + 2 > 0 and x^2 −bx + 8 ≥ 0 for all real numbers x, then the largest possible value of 2a−6b is?
Answer: 36
Solution: Given,
2x^2 −ax + 2 > 0
2{ (x-a/4)^2 - a^2/16+1} > 0 ∀ x ∈R
-a^2/16+1 > 0
a ∈{ -3,-2,-1,0,1,2,3}
x^2 −bx + 8 ≥ 0
(
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