Question

the value of λ for which the quadratic equation x² - 8x + λ = 0 has unequal and real roots is :​

Answer 1

Answer:

real and unequal roots for all λ∈R−{−1}

x

2

−6x+8+λ(x

2

−4x+3)=0

⇒(1+λ)x

2

−2(3+2λ)x+(8+3λ)=0

Discriminant of above quadratic equation is,

Δ=4(3+2λ)

2

−4(1+λ)(8+3λ)

=4[(3+2λ)

2

−(1+λ)(8+3λ)]

=4[4λ+12λ+9−(3λ

2

+11λ+8)]

=4(λ

2

+λ+1)

Now, since discriminant of quadratic λ

2

+λ+1=0 is negative,

Δ>0 for all λ∈R−{−1}

Hence, roots are real and unequal.

Hence, first option is correct.