2018 · Q16
If α and β are the roots of ax² + bx + c = 0, then the value of 1/(aα + b) + 1/(aβ + b) is
Elementary MathematicsAlgebra
- Aa/(bc)
- Bb/(ac)
- Cc/(ab)
- D1/(abc)
Explanation
Since alpha is a root, a*alpha^2 + b*alpha + c = 0, i.e. a*alpha + b = -c/alpha, so 1/(a*alpha + b) = -alpha/c; likewise 1/(a*beta + b) = -beta/c. Their sum is -(alpha + beta)/c = -(-b/a)/c = b/(ac), using alpha + beta = -b/a. Hence option B.