Quantitative Aptitude – Quadratic Equations – The number of solution to the equation
Slot – 1 – Quantitative Aptitude – Quadratic Equations – The number of solution to the equation
The number of solution to the equation – Video
Q. The number of solution to the equation |x| (6x^2 + 1) = 5x^2 is?
Answer: 5
Solution:
case 1) If x >0
X*(6x^2 +1) = 5x^2
6x^3 -5x^2 +x = 0
x(6x^2 -5x +1) = 0
x(6x^2 -3x -2x +1) =0
x(2x -1)*(3x -1) =0
x = 0, ½ or 1/3
number of solutions = 3
case 2) if x < 0
– X*(6x^2 +1) = 5x^2
6x^3 + 5x^2 +x = 0
x(6x^2 +5x +1) = 0
x(6x^2 +3x +2x +1) =0
x(2x +1)*(3x +1) =0
x = 0, -1/2 or -1/3
Thus x can take 5 different values 0,1/2, 1/3, -1/2 and -1/3
Total number of solutions = 5