TS EAMCET · Maths · Quadratic Equation
The condition to be satisfied in order that one root of \(x^3+b x^2+c x+d=0\) is the sum of the other two roots, is
- A \(3 d^2+b^3=b^2 c\)
- B \(6 d+b^3=2 b c\)
- C \(8 d+b^3=4 b c\)
- D \(8 d+b^2=4 b c\)
Answer & Solution
Correct Answer
(C) \(8 d+b^3=4 b c\)
Step-by-step Solution
Detailed explanation
Let, for the equation \(x^3+b x^2+c x+d=0\) having roots \(\alpha, \beta\) and \(\gamma\). So, \(\alpha+\beta+\gamma=-b\) and according to given information, Let \(\alpha=\beta+\gamma\) from Eqs. (i) and (ii), we get \(2 \alpha=-b \Rightarrow \alpha=-\frac{b}{2}\)…
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