Question

8.Equation (x+1)2 – x2 = 0 has _____ real root(s). *

1 point

(A) 1

(B) 2

(C) 3

(D) 4​

Answer 1

Answer:

no roots

Step-by-step explanation:

Given equation is (x

2

+1)

2

−x

2

=0

⇒(x

2

)

2

+(1)

2

+2(x)

2

(1)−x

2

=0

⇒(x

2

)

2

+x

2

+1=0

Let x

2

=y

⇒y

2

+1y+1=0

Now, D=b

2

−4ac

⇒D=(1)

2

−4(1)(1)=1−4

⇒D=−3

⇒D<0

So, the given equation y

2

+y+1=0 has no real roots.

∴ the equation $$\left ( x^{2} + 1 \right )^{2} - x^{2} =0$ has no real roots.

Hence, the correct answer is option [C].