JEE Main 2020 (Online) 6th September Evening ShiftQuestion 1
If $\alpha$ and $\beta$ are the roots of the equation $2x(2x+1)=1$, then $\beta$ is equal to :
Quadratic Equation · Relation Between Roots and Coefficients
Solution
Concept. $\beta=-\frac12-\alpha$; use $4\alpha^2=1-2\alpha$ to turn an option into this. Formulas used. (1) $4x^2+2x-1=0$: sum of roots $-\frac12$Step 1 - $\beta$. By (1), $\beta=-\frac12-\alpha$. Step 2 - Check (B). $\alpha$ is a root, so $2\alpha^2=\frac12-\alpha$. Then $$-2\alpha(\alpha+1)=-2\alpha^2-2\alpha=-\frac12+\alpha-2\alpha=-\frac12-\alpha=\beta.$$ Answer: (B)