JEE Main 2022 · 30 Jun · Shift 1 · Mathematics Q4

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MathematicsSingle correct+4 / -1Question 4 of 90

Let $A=\begin{bmatrix}1&-2&\alpha\\\alpha&2&-1\end{bmatrix}$ and $B=\begin{bmatrix}2&\alpha\\-1&2\\4&-5\end{bmatrix}$ , $\alpha\in\mathbf C$ . Then the absolute value of the sum of all values of $\alpha$ for which $\det(AB)=0$ is :

Answer and worked solution

Official answer: A

Determinant. $\det(AB)=4\alpha^3+12\alpha^2+20\alpha+12=4(\alpha+1)(\alpha^2+2\alpha+3)$ .

Roots $-1$ and $-1\pm i\sqrt2$ : sum $-3$ , absolute value 3.

(A)

Topics:Determinants and properties Theory of equations (higher degree)

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JEE Main 2022 · 30 Jun · Shift 1, Mathematics question 4