AP EAMCET · Maths · Quadratic Equation
If -1 is a twice repeated root of the equation \(a x^3+b x^2+c x+1=0\), then
- A \(\mathrm{b}=2 \mathrm{a}+1, \mathrm{c}=\mathrm{a}+1\)
- B \(\mathrm{b}=2 \mathrm{a}+1, \mathrm{c}=\mathrm{a}-2\)
- C \(\mathrm{b}=2 \mathrm{a}+1, \mathrm{c}=\mathrm{a}+2\)
- D \(b=2 a-1, c=a+2\)
Answer & Solution
Correct Answer
(C) \(\mathrm{b}=2 \mathrm{a}+1, \mathrm{c}=\mathrm{a}+2\)
Step-by-step Solution
Detailed explanation
Let roots of equation be \(-1,-1, \alpha\) Now, \(\alpha=\frac{-1}{a}\) and \(-1-1-\frac{1}{a}=\frac{-b}{a}\) \(\Rightarrow b=2 a+1\) and \(-a+b-c+1=0 \Rightarrow c=-a+b+1\) \(\Rightarrow c=a+2\)
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