TS EAMCET · Maths · Quadratic Equation
If the roots of \(x^4+x^3-4 x^2+x+1=0\) are diminished by \(\alpha\) or \(\beta\), then the equation with the diminished roots does not contain \(x^2\) term. Then \(12(\alpha-\beta)^2=\)
- A \(35\)
- B \(105\)
- C \(96\)
- D \(115\)
Answer & Solution
Correct Answer
(A) \(35\)
Step-by-step Solution
Detailed explanation
Let the roots of equation \(x^4+x^3-4 x^2+x+1=0\) are diminished by \(h\), so the equation becomes \((x+h)^4+(x+h)^3-4(x+h)^2+(x+h)+1=0\) Now the coefficient of \(x^2\) is \(6 h^2+3 h-4\) must be zero \(\therefore \quad 6 h^2+3 h-4=0\) having roots \(\alpha\) and \(\beta\) So,…
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