Question

Consider the quadratic equation $a{x}^2+bx+(a^2+b^2+c^2-ab-bc-ca)=0$ (where $a,b,c$ are distinct real numbers)

If the equation does not have any real roots then which of the following is always true.

• A. $b>0$
• B. $b<0$
• C. $a>0$
• D. $a<0$

Answer 1

The correct option is C $a>0$

For the equation $a{x}^2+bx+(a^2+b^2+c^2-ab-ac-bc)=0$ not to have real roots , the determinant must be greater than zero and the value of $a$ must be greater than zero

Therefore $a>0$ is always true

So the correct option is $C$