AP EAMCET · Maths · Quadratic Equation
Which among the following equations has roots which are negatives of the roots of the equation \(x^3-x^2+x-4=0\) ?
- A \(x^3-x^2+x-4=0\)
- B \(x^3+x^2+x+4=0\)
- C \(x^3-x^2+x-4=0\)
- D \(x^3-x^2-x-4=0\)
Answer & Solution
Correct Answer
(B) \(x^3+x^2+x+4=0\)
Step-by-step Solution
Detailed explanation
Let \(\alpha\) is the root of equation \(x^3-x^2+x-4=0\) Now, put \((-\alpha)=x\), so we get the required equation, and it is \(\begin{aligned} & (-x)^3-(-x)^2+(-x)-4=0 \\ & \Rightarrow \quad-x^3-x^2-x-4=0 \\ & \Rightarrow \quad x^3+x^2+x+4=0 \\ \end{aligned}\)
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