Question

find the roots of quadratic equation x^2 + 1/x^2 + 5(x + 1/x) +4 = 0

Answer 1

Question

Without solving the following quadratic equation, find the value of m for which the given equation has real and equal roots.

x

2

+2(m−1)x+(m+5)=0

Easy

Solution

The given equation is x

2

+2(m−1)x+(m+5)=0

For the equation to have real and equal roots, the discriminant should be 0.

∴[2(m−1)]

2

−4(m+5)=0

⇒4(m

2

−2m+1)=4(m+5)

⇒m

2

−3m−4=0

⇒(m−4)(m+1)=0

∴m=4 or m=−1