Question

7. Find the number of real roots of equation (x²+ 3)²- x² = 0


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Answer 1

$x2+1)2−x2=0</p><p></p><p>⇒(x2)2+(1)2+2(x)2(1)−x2=0</p><p></p><p>⇒(x2)2+x2+1=0</p><p></p><p></p><p>Let x2=y</p><p></p><p>⇒y2+1y+1=0</p><p></p><p>Now, D=b2−4ac</p><p></p><p>⇒D=(1)2−4(1)(1)=1−4</p><p></p><p>⇒D=−3</p><p></p><p>⇒D<0</p><p></p><p>So, the given equation y2+y+1=0 has no real roots.</p><p></p><p>∴ the equation \left ( x^{2} + 1 \right )^{2} - x^{2} =0 has no real roots.</p><p></p><p>$

Answer 2

Answer:

Correct option is

C

no real roots

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]

Hope it helps you.