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) is equal to

• A. 0
• B. a + c
• C. ac
• D. -ac

Answer 1

Answer: (C)

ac

Answer 2

The second equation having equal roots implies its discriminant is zero, leading to $a^2=4b$. The root of this equation is $a/2$. Since this is the common root, $a/2$ must satisfy the first equation. Substituting $x=a/2$ into the first equation and using $a^2=4b$, we derive $2(b+d)=ac$.