AP EAMCET · Maths · Quadratic Equation
If -1 is a twice repeated root of the equation \(a\left(x^3+x^2\right)+\) \(\mathrm{bx}+\mathrm{c}=0\), then \(\mathrm{a}: \mathrm{b}: \mathrm{c}=\)
- A \(:-1: 1\)
- B \(-1: 1: 1\)
- C \(1: 1:-1\)
- D \(1: 1: 1\)
Answer & Solution
Correct Answer
(B) \(-1: 1: 1\)
Step-by-step Solution
Detailed explanation
Since \(x=1\) is a twice repeated root of \(f(x)=a x^3+a x^2\) \(+b x+c=0\). Hence \(f(-1)=0\) and \(f^{\prime}(-1)=0\) Now \(f(-1)=0\) \[ \Rightarrow-a+a+b+c=0 \Rightarrow c=b \] Now \(f^{\prime}(x)=3 a x^2+2 a x+b\)…
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