Question

For the quadratic equation $2x^2+6\sqrt{2}x+1=0$

• A. roots are rational
• B. if one root is $p+\sqrt{q}$, then the other is $-p+\sqrt{q}$
• C. roots are irrational
• D. if one root is $p+\sqrt{q}$, then the other is $p-\sqrt{q}$

Answer 1

Answer: (C), (D)

The correct options are
C roots are irrational
D if one root is $p+\sqrt{q}$, then the other is $p-\sqrt{q}$

Here,

$2x^2+6\sqrt{2x}+1=0$

$\Rightarrow x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}=\frac{-6\sqrt{2}\pm \sqrt{64}}{4}=\frac{-3\sqrt{2}\pm 4}{2}$

Therefore, roots are irrational.

If $p=-\frac{3\sqrt{2}}{2}$ and $q=4$

One root is $p+\sqrt{q}$, then the other root is $p-\sqrt{q}$

Ans: C,D