Question

If the roots $x_1$ and $x_2$ of the quadratic equation $x^2 - 2x + c = 0$ also satisfy the equation $7x_2 - 4x_1 = 47$, then which of the following is true?

• A. $c = -15$
• B. $x_1 = -5, x_2 = 3$
• C. $x_1 = 4.5, x_2 = -2.5$
• D. None of these

Hint:

Use sum and product of roots directly from the quadratic equation coefficients.

Answer 1

The Correct Option is A

From $x^2 - 2x + c = 0$, sum of roots $x_1 + x_2 = 2$, product $x_1 x_2 = c$. Also $7x_2 - 4x_1 = 47$. Sub $x_2 = 2 - x_1$: $7(2 - x_1) - 4x_1 = 47 \Rightarrow 14 - 7x_1 - 4x_1 = 47 \Rightarrow -11x_1 = 33 \Rightarrow x_1 = -3$. Then $x_2 = 2 - (-3) = 5$. Product = $(-3)(5) = -15 \Rightarrow c = -15$.