2022 · Q38
What is the condition that the roots of the equation ax² + bx + c = 0 are in the ratio c : 1?
Elementary MathematicsAlgebra
- Ab² = a(c + 1)²
- Ba² = b(c + 1)²
- Cb² = a(c - 1)²
- Dab² = (c + 1)²
Explanation
Let the roots be ck and k (ratio c:1). Then k(c+1) = -b/a and ck² = c/a, so k² = 1/a. Substituting gives (c+1)²/a = b²/a², i.e. b² = a(c+1)². Hence the keyed option is A.