CUET · MATHS · PYQ PAPER 2025
If \(x=-4\) is a root of \(\left|\begin{array}{lll}x & 2 & 3 \\ 1 & x & 1 \\ 3 & 2 & x\end{array}\right|=0\) , then the sum of the other two roots is
- A 4
- B -3
- C 2
- D 5
Answer & Solution
Correct Answer
(A) 4
Step-by-step Solution
Detailed explanation
\(x(x^2 - 2) - 2(x - 3) + 3(2 - 3x) = 0\) \(x^3 - 2x - 2x + 6 + 6 - 9x = 0\) \(x^3 - 13x + 12 = 0\) Sum of roots \(= -\frac{\text{coefficient of } x^2}{\text{coefficient of } x^3}\) \(-4 + \beta + \gamma = -\frac{0}{1}\) \(-4 + \beta + \gamma = 0\) \(\beta + \gamma = 4\)
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