Question

For$f\left(x\right)=a{x}^2+bx+c,a\ne 0,$ the conditions for which the graph is a downward opening parabola and f(x)=0 have a unique root with multiplicity $2$ is (Here D=discriminant)

• A. $a>0,D<0$
• B. $a<0,D<0$
• C. $a<0,D=0$
• D. $a>0,D=0$

Answer 1

The correct option is C $a<0,D=0$

Given: $y=a{x}^2+bx+c,a\ne 0$
For graph to be a downward opening parabola we must have $a<0$
Also, the equation has one root with a multiplicity 2, meaning the equation has identical real roots. Which occurs when
Discriminant$\left(D\right)=0$