Question

If x = -9 is a root of A = $\left|\begin{array}{ccc}x& 3& 7\\ 2& x& 2\\ 7& 6& x\end{array}\right|$ = 0, then other two root are

• A. 3,7
• B. 2,7
• C. 3,6
• D. 2,6

Answer 1

Answer: (B)

GivenA = $\left|\begin{array}{ccc}x& 3& 7\\ 2& x& 2\\ 7& 6& x\end{array}\right|$ = 0
$\Rightarrow$ x[x ² - 12] - 3[2x- 14] + 7[12 - 7x] = 0
$\Rightarrow x^3$ - 67x + 126 = 0
But given (x = 9) is a root of given determinant
$\therefore (x+9)$is a factor
$\Rightarrow x^3+9x^2-9x^2-$81x + 14x + 126 = 0
$\Rightarrow x^2$(x + 9) - 9x(x + 9) + 14(x + 9) = 0
$\Rightarrow (x+9)(x^2$-9x +14)=0
$\Rightarrow (x+9)(x^2$-7x -2x+14)=0
$\Rightarrow$ (x + 9) (x - 7) (x - 2) = 0
$\Rightarrow x=-9,7,2$