Question

Determine the nature of roots of the below equation? 
$x ^{2} - 4x + 4 = 0$
​

Answer 1

Answer:

10th

Maths

Quadratic Equations

Nature of Roots

The equation x^2 - 6x + 8 +...

MATHS

The equation x

2

−6x+8+λ(x

2

−4x+3)=0,∀λ∈R−{−1} has

HARD

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VIDEO EXPLANATION

ANSWER

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}