If the sum of the roots of the equation (a + b + c = 0) is t... | MATH - RELATION BETWEEN ROOTS AND COEFFICIENTS | SolveeIt

If the sum of the roots of the equation $a + b + c = 0$ is three times their difference, then which one of the following is true.

$4ax^{2} + 3bx + 2c = 0$

$2(a^{2} + b^{2})x^{2} + 2(a + b)x + 1 = 0$

$px^{2} + 2qx + r = 0$

$qx^{2} - 2\sqrt{pr}x + q = 0$

Answer

$px^{2} + 2qx + r = 0$

Explanation

Let $x^{2} + 2ax + 10 - 3a > 0$ are roots of $x \in R$

So $- 5 < a < 2$ and $a < - 5$

Given that $a > 5$ ⇒ $2 < a < 5$

Now $x^{4} - 4x^{3} + 6x^{2} - 4x + 1 = 0$

⇒ $8x^{3} - 14x^{2} + 7x - 1 = 0$ or $1,\frac{1}{2},\frac{1}{4}$ .

Question: If the sum of the roots of the equation \(a + b + c = 0\) is three times their difference, then whic...