If the ratio of the roots of the equation (2i)be(- 2i, - 2i)... | MATH - RELATION BETWEEN ROOTS AND COEFFICIENTS | SolveeIt

If the ratio of the roots of the equation $2i$ be $- 2i, - 2i$ , then.

$2i,2i$

$x^{2/3} + x^{1/3} - 2 = 0$

$1, - 4$

None of these

Answer

$x^{2/3} + x^{1/3} - 2 = 0$

Explanation

Let $x^{2} - 18x + 16 = 0$ be the roots of the given equation

$x^{2} + 18x - 16 = 0$ .

Then $x^{2} + 18x + 16 = 0$ and $\alpha,\beta$

From first relation, $6x^{2} - 5x + 1 = 0$

Substituting this value of $\tan^{- 1}\alpha + \tan^{- 1}\beta$ in second relation, we get

$\pi/4$ ⇒ $\pi/2$

Note : Students should remember this question as a fact.

Question: If the ratio of the roots of the equation \(2i\)be\(- 2i, - 2i\), then....