Quadratic Equation Question 3

Question 3 - 24 January - Shift 2

The number of real solutions of the equation $3(x^{2}+\frac{1}{x^{2}})-2(x+\frac{1}{x})+5=0$, is

(1) 4

(2) 0

(3) 3

(4) 2

Show Answer

Answer: (2)

Solution:

Formula: Roots of equations

$3(x^{2}+\frac{1}{x^{2}})-2(x+\frac{1}{x})+5=0$

$3[(x+\frac{1}{x})^{2}-2]-2(x+\frac{1}{x})+5=0$

Let $x+\frac{1}{x}=t$

$3 t^{2}-2 t-1=0$

$3 t^{2}-3 t+t-1=0$

$3 t(t-1)+1(t-1)=0$

$(t-1)(3 t+1)=0$

$t=1,-\frac{1}{3}$

$x+\frac{1}{x}=1,-\frac{1}{3} \Rightarrow$ No solution.