TS EAMCET · Maths · Quadratic Equation
If \(1+2 i\) is a root of the equation \(x^4-3 x^3+8 x^2-7 x+5=0\), then sum of the squares of the other roots is
- A 0
- B 2+i
- C -4-4i
- D \(\frac{8}{3}\)
Answer & Solution
Correct Answer
(C) -4-4i
Step-by-step Solution
Detailed explanation
Let the roots be \(x_1, x_2, x_3, x_4\). Given root: \(x_1 = 1+2i\). Since coefficients are real, the conjugate is also a root: \(x_2 = 1-2i\). The quadratic factor with roots \(x_1, x_2\) is \(x^2 - (x_1+x_2)x + x_1x_2 = x^2 - (1+2i+1-2i)x + (1+2i)(1-2i)\). \(= x^2 - 2x + 5\).…
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