Question

In a quadratic function, recall that the discriminant D = b2 - 4ac. For which function is it true that a < 0 and D = 0?

Answer 1

If D = 0, then the quadratic equation has 1 solution x = − b/2a

Explanation:

If we have a quadratic equation x² +3x-4= 0

Then the corresponding values of a= 1, b=3, c= -4

Finding the discriminant gives

D= b2 - 4ac.

D= 3²- 4(1) (-4)

D= 9 + 16

D= 25

Here a> 0

But if a< 0 e.g a= -1

D= b2 - 4ac.

D= 3²- 4(-1) (-4)

D= 9 - 16

D= -7

Here a < 0 so we get the answer -7 < 0

D= b2 - 4ac.

D= 4²- 4(-1) (-4)

D= 16 - 16

D= 0

Here a< 0 and b= - c so that D= 0

When D < 0 roots do not exist.

If D = 0, then the quadratic equation has 1 solution x = − b/2a

This can be found out by using the quadratic formula

x= -b±√b²- 4ac/ 2a

But D= 0

x= -b±0/ 2a

x= -b/2a

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