Solveeit Logo
Login

Question

Mathematics Question on Quadratic Equations

If a and ??are the roots of 4x2 + 2x + 1 = 0, then ??=

A

−14α-\frac{1}{4\alpha}

B

−12α-\frac{1}{2\alpha}

C

−1α-\frac{1}{\alpha}

D

−13α-\frac{1}{3\alpha}

Answer

−14α-\frac{1}{4\alpha}

Explanation

Solution

Given equation is 4x2+2x−1=04 x^{2}+2 x-1=0 Roots of the equation are α\alpha and β\beta. ∴α+β=−ba=−24=−12\therefore \alpha+\beta=\frac{-b}{a}=\frac{-2}{4}=-\frac{1}{2} and αβ=Ca=−14 \alpha \beta=\frac{C}{a}=-\frac{1}{4} ∴β=−14α\therefore \beta=-\frac{1}{4 \alpha}