Question

Assertion :If trace of the matrix $\left[\begin{array}{cccc}x-5& 0& 2& 4\\ 3& x^2-10& 6& 1\\ -2& 3& x-7& 1\\ 1& 2& 0& -2\end{array}\right]$ is zero,then value of x is -6 or 4 Reason: Distinct roots of a quadratic equation $a{x}^2+bx+c=0$ are possible if discriminant of the equation is positive i.e, $b^2-4ac>0$

• A. Both (A) & (R) are individually true & (R) is correct explanation of (A),
• B. Both (A) & (R) are individually true but (R) is not the correct (proper) explanation of (A).
• C. (A)is true but (R} is false,
• D. (A)is false but (R} is true.

Answer 1

The correct option is B Both (A) & (R) are individually true but (R) is not the correct (proper) explanation of (A).

Trace of Given matrix is $0$.
$\therefore x-5+x^2-10+x-7+(-2)=0\Rightarrow x^2+2x-24=0$ $(\because D=\sqrt{4+96}=10>0)\therefore$ Roots are distinct $\therefore (x-4)(x+6)=0\therefore x=-6,4$
Assertion (A) & Reason (R) both are individually true but Reason (R) is not the correct explanation of the Assertion (A)
Hence, option B.