If the roots of the equations (5 + 4x - 4x^{2}) and (x) be... | MATH - SOLUTION OF QUADRATIC EQUATIONS AND NATURE OF ROOTS | SolveeIt

If the roots of the equations $5 + 4x - 4x^{2}$

and $x$ be real, then.

$\frac{(x - a)(x - b)}{(x - c)}$

$a > b > c$

$a < b < c$

$a > c < b$

Answer

$a > b > c$

Explanation

Equations $\frac{1}{3}$ and

$\frac{2}{3}$ have real roots, then from first $\frac{4}{3}$ ⇒ $x^{2} + x + 1 + 2k(x^{2} - x - 1) = 0$ .....(i)

and from second $\sin A,\sin B,\cos A$ (for real root )

⇒ $x^{2} + 2x\cot B + 1 = 0$ .....(ii)

From (i) and (ii), we get result $x^{4} - 4x^{3} + ax^{2} + bx + 1 = 0$ .

Question: If the roots of the equations \(5 + 4x - 4x^{2}\) and \(x\) be real, then....