$∣ ∣ ∣ ∣ \begin{matrix} x + 2 & x + 3 & x + 5 x + 4 & x + 6 & x + 9 x + 8 & x + 11 & x + 15 \end{matrix} ∣ ∣ ∣ ∣$ =

3 x^{2} + 4 x + 5

No worries! We‘ve got your back. Try BYJU‘S free classes today!

x^{3} + 8 x + 5

No worries! We‘ve got your back. Try BYJU‘S free classes today!

0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

- 2

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is B $- 2$
$∣ ∣ ∣ ∣ \begin{matrix} x + 2 & x + 3 & x + 5 x + 4 & x + 6 & x + 9 x + 8 & x + 11 & x + 15 \end{matrix} ∣ ∣ ∣ ∣$ $= ∣ ∣ ∣ ∣ \begin{matrix} x + 2 & x + 3 & x + 5 2 & 3 & 4 4 & 5 & 6 \end{matrix} ∣ ∣ ∣ ∣, R_{3} \to R_{3} - R_{2}, R_{2} \to R_{2} - R_{1}$
$= (x + 2) (18 - 20) - (x + 3) (12 - 16) + (x + 5) (10 - 12)$ , Expand along first row
$= - 2 x - 4 + 4 x + 12 - 2 x - 10 = - 2$

Suggest Corrections