What is the condition that the roots of the equation ax^2+bx+c=0 are in the ratio c:1?
- A. b^2=a(c+1)^2 ✓
- B. a^2=b(c+1)^2
- C. b^2=a(c-1)^2
- D. ab^2=(c+1)^2
Correct Answer: A. b^2=a(c+1)^2
Explanation
Let the roots be r and cr. Sum: r(1+c) = -\frac{b}{a} \implies r = -\frac{b}{a(c+1)}. Product: r^2c = \frac{c}{a} \implies r^2 = \frac{1}{a}. Equating r^2 gives \frac{b^2}{a^2(c+1)^2} = \frac{1}{a} \implies b^2 = a(c+1)^2.
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