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Q.

Consider the following statements in respect of the given equation:

1) All the roots of the equation are complex.

2) The sum of all the roots of the equation is 6.

Which of the above statements is/are correct?

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a

1 only

b

2 only

c

Both 1 and 2

d

Neither 1 nor 2

answer is B.

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Detailed Solution

Concep- We obtain the value of a given polynomial at any two points, and if the values have opposite signs, we know that the function has a value of 0 somewhere between these two points. If the polynomial seems to be zero at any point, that point is the root of the given polynomial.
Let

x 2 + 2 = y

The given equation becomes

8 x 2 + y 2 − 6 x y = 0

⇒ (y − 4 x) (y − 2 x) = 0

⇒ y = 4 x, y = 2 x

Since

y = x 2 + 2

⇒ x 2 − 4 x + 2 = 0, x 2 − 2 x + 2 = 0

x = 2 ± 2, 1 ± i

.All the roots are not complex
Sum of all the roots

= 6

So, statement 2 is only correct
Hence, option 2 is correct.

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