Question

If the two equations $x^2-cx+d=0$ and $x^2-ax+b=0$ have one common root and the second has equal roots, then $2(b+d)=$)

• A. 0
• B. a+c
• C. ac
• D. -ac

Answer 1

The correct option is C

ac

Let roots of $x^2-cx+d=0$ be α, β then roots of $x^2-ax+b=0$ be α, α

∴ α + β = c, αβ = d, α + α = α, ${\alpha }^2$ = b

Hence $2(b+d)=2({\alpha }^2+\alpha \beta )=2\alpha (\alpha +\beta )=ac$