AP EAMCET · Maths · Quadratic Equation
If the equation \(x^4+a x^3+b x^2+c x+d=0\) has three equal roots, then that root is
- A \(\frac{6 c-a b}{8 b-3 a^2}\)
- B \(\frac{a b-6 c}{8 b+3 a^2}\)
- C \(\frac{6 \mathrm{c}-\mathrm{ab}}{3 \mathrm{a}^2-4 \mathrm{~b}}\)
- D \(\frac{6 c-a b}{3 a^2-8 b}\)
Answer & Solution
Correct Answer
(D) \(\frac{6 c-a b}{3 a^2-8 b}\)
Step-by-step Solution
Detailed explanation
Let \(\alpha, \alpha, \alpha, \beta\) be the roots of given equation \[ x^4+a x^3+b x^2+c x+d=0 \] Hence \(3 \alpha+\beta=-a, \quad 3 \alpha(\alpha+\beta)=b\) \[ \alpha^2(\alpha+3 \beta)=-c, \quad \alpha^3 \beta=d \] Now consider…
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