Home › MCQs › EEJ MAIN Mathematics › Question #6022
Back to Questions
EEJ MAIN Mathematics QUESTION #6022
Question 1

If the determinant $\begin{vmatrix}x-4&2x&2x\\2x&x-4&2x\\2x&2x&x-4\end{vmatrix} = (A+Bx)(x-A)^2$, find the ordered pair $(A,B)$.

  • $(-4,5)$✔️
  • $(4,5)$
  • $(-4,-5)$
  • $(-4,3)$
Correct Answer Explanation

Apply $R_1\to R_1+R_2+R_3$: each element in row 1 becomes $5x-4$.

Factor out $(5x-4)$: $\Delta = (5x-4)\begin{vmatrix}1&1&1\\2x&x-4&2x\\2x&2x&x-4\end{vmatrix}$

Apply $C_2-C_1, C_3-C_1$: $= (5x-4)\begin{vmatrix}1&0&0\\2x&-x-4&0\\2x&0&-x-4\end{vmatrix} = (5x-4)(x+4)^2$

Comparing with $(A+Bx)(x-A)^2$: $A=-4$, $B=5$. So $(A,B)=\mathbf{(-4,5)}$.