Question

For which discriminant is the graph possible

b2-4ac=0

b2-4ac=-1

b2-4ac=4

Answer 1

"
`b^2-4ac=4`"

Explanation:

By looking at the value of the discriminant in a quadratic, we can find the nature of roots.

Let the value of the discriminant be "D", so we can say:

• D > 0 [2 distinct real roots]
• D = 0 [2 same real roots]
• D < 0 [no real roots]

Graphically, we can write the points in order as:

• D > 0, 2 cutting point in x-axis
• D = 0, 1 touching point in x-axis
• D < 0, NO cutting/touching point in x-axis

Looking at the graph, we clearly see that there is 2 cutting points in the x-axis, so there are 2 roots. This means the value of the discriminant should be greater than 0 (positive value).

Out of the 3 choices given with discriminant formula, the last one has a value that is greater than 0:

4 > 0

Hence, last answer choice is right.