AP EAMCET · Maths · Quadratic Equation
The cubic equation whose roots are the squares of the roots of the equation \(x^3-2 x^2+3 x-4=0\) is
- A \(x^3+2 x^2+7 x-16=0\)
- B \(x^3+2 x^2-7 x-16=0\)
- C \(x^3-2 x^2-7 x+16=0\)
- D \(x^3-2 x^2+7 x+16=0\)
Answer & Solution
Correct Answer
(B) \(x^3+2 x^2-7 x-16=0\)
Step-by-step Solution
Detailed explanation
\(x^3-2 x^2+3 x-4=0 \Rightarrow x^3+3x = 2x^2+4\) Let \(y=x^2\). Squaring \(x(x^2+3) = 2x^2+4\): \(y(y+3)^2 = (2y+4)^2\) \(y(y^2+6y+9) = 4(y^2+4y+4) \Rightarrow y^3+6y^2+9y = 4y^2+16y+16 \Rightarrow y^3+2y^2-7y-16=0\) The cubic equation is \(x^3+2x^2-7x-16=0\).
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