Q. If the difference of the roots of the equation $x^{2} - bx + c = 0$ be 1, then
A) $b^{2} - 4c - 1 = 0$
B) $b^{2} - 4c = 0$
C) $b^{2} - 4c + 1 = 0$
D) $b^{2} + 4c - 1 = 0$
Explanation
(a)
Let $\alpha\ and\ \beta$ be the roots of the equation $x^{2} - bx + c = 0$.
$\Rightarrow \ \alpha + \beta = b\ and\ \alpha\beta = c$
$\therefore\ \alpha - \beta = \sqrt{(\alpha + \beta)^{2} - 4\alpha\beta}$
$\Rightarrow 1 = \sqrt{b^{2} - 4c}$
$\Rightarrow b^{2} - 4c - 1 = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.