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Consider the following statements in respect of the given
equation
$\left(x^{2}+2\right)^{2}+8 x^{2}=6 x\left(x^{2}+2\right)$
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?
Options:
equation
$\left(x^{2}+2\right)^{2}+8 x^{2}=6 x\left(x^{2}+2\right)$
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?
Solution:
1719 Upvotes
Verified Answer
The correct answer is:
2 only
$\quad\left(x^{2}+2\right)^{2}+8 x^{2}=$2
$+8 x^{2}$
$y^{2}-6 x y+8 x$
$y=\frac{6 x \pm \sqrt{36 x^{2}-32 x^{2}}}{2}$
$y=4 x$
At
$x^{2}-4 x+2=0$
Discriminant, $\mathrm{D}=$
Roots are real Sum of roots $=-(-4)$
At
$\mathrm{D}=4-8=-$
Roots are complex Sum of roots $=$ Sum of all roots $=4+2=6$ only statement 2 is (b)
$+8 x^{2}$
$y^{2}-6 x y+8 x$
$y=\frac{6 x \pm \sqrt{36 x^{2}-32 x^{2}}}{2}$
$y=4 x$
At
$x^{2}-4 x+2=0$
Discriminant, $\mathrm{D}=$
Roots are real Sum of roots $=-(-4)$
At
$\mathrm{D}=4-8=-$
Roots are complex Sum of roots $=$ Sum of all roots $=4+2=6$ only statement 2 is (b)
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