Question

If $a>0$ and discriminant of $a{x}^2+2bx+c<0$ is greater than zero, then $\left|\begin{array}{ccc}a& b& ax+b\\ b& c& bx+c\\ ax+b& bx+c& 0\end{array}\right|$ is

• A. positive
• B. $(ac-b^2)(a{x}^2+2bx+c)$
• C. negative
• D. 0

Answer 1

Answer: (C)

negative

It is given that

$a>0,4b-4ac<0$

when we expand the equation we have to use $a>0,b^2-ac<0$, use it and you will get the value of the determinant as 0

then obviously the $\left|\begin{array}{ccc}a& b& ax+b\\ b& c& bx+c\\ ax+b& bx+c& 0\end{array}\right|$ will be negative.