AP EAMCET · Maths · Quadratic Equation
The equation \(6 x^4-5 x^3+13 x^2-5 x+6=0\) will have
- A only real roots
- B only complex roots
- C two real and two complex roots
- D two real and two purely imaginary roots
Answer & Solution
Correct Answer
(B) only complex roots
Step-by-step Solution
Detailed explanation
\(6(x^2+1/x^2)-5(x+1/x)+13=0\) Let \(y=x+1/x \implies x^2+1/x^2=y^2-2\) \(6(y^2-2)-5y+13=0 \implies 6y^2-5y+1=0\) \(y = \frac{-(-5) \pm \sqrt{(-5)^2-4(6)(1)}}{2(6)} = \frac{5 \pm \sqrt{25-24}}{12} = \frac{5 \pm 1}{12}\) \(y_1=1/2, y_2=1/3\) For \(x^2-yx+1=0\), the discriminant…
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