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CBSE Class 12 Math 2022 Term I Solved Paper

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Question : 39 of 50
Marks: +1, -0
If x=−4x=-4 is a root of ∣x231x132x∣=0\begin{vmatrix} x & 2 & 3 \\ 1 & x & 1 \\ 3 & 2 & x \end{vmatrix}=0, then the sum of the other two roots is
Solution:     👈: Video Solution
   Explanation: Given,   ∣x231x132x∣=0\;\text{ Explanation: Given, }\; \begin{vmatrix} x & 2 & 3 \\ 1 & x & 1 \\ 3 & 2 & x \end{vmatrix}=0
⇒    x(x2−2)−2(x−3)+3(2−3x)\Rightarrow\;\; x (x^2-2)-2(x-3)+3(2-3x)
⇒    x3−13x+12=0\Rightarrow\;\; x^3-13x+12=0
Since (x+4)(x+4) is one root of above cubic equation.
   Sum roots   =0\;\text{ Sum roots }\;=0
∴    \therefore\;\; Sum of two roots +(−4)=0+(-4)=0
Sum of two roots =4=4
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