First slide

Introduction to Determinants

Question

Let
$P (x) = |\begin{array}{ccc} 7 & 6 & x - 10 \\ 2 & x - 10 & 5 \\ x - 10 & 3 & 4 \end{array}|$
sum of zeros of $P (x)$ is

Moderate

A

30
B

28
C

27
D

25

Solution

Using $R_{1} \leftrightarrow R_{3}$ write
$P (x) = - |\begin{array}{ccc} x - 10 & 3 & 4 \\ 2 & x - 10 & 5 \\ 7 & 6 & x - 10 \end{array}|$
$∴$ sum of zeros of $P (x)$
$= - \frac{coefficient of x^{2}}{coefficient of x^{3}} = 30$

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