Help Calculate the value of the discriminant?

Question

a. Calculate the value of the discriminant of x^2+4x+4
b.By examining the sign of the discriminant in part a, how many x-intercepts would the graph of have? Why?

Answer 1

Hi,

For a quadratic equation like ax² + bx = c = 0, the discriminant is found by computing b² - 4ac. For x² + 4x + 4, the discriminant is:

b² - 4ac =
4² - 4*1*4 =
16 - 16 = 0 <== discriminant value

If the discriminant was any negative number, there would be 2 complex roots with "i".

When the discriminant is zero as it is here, there is only one real root. <== answer to part b

If the discriminant was any positive number, there would be 2 real roots.

I hope that helps!! :-)

Answer 2

The discriminant = b²-4ac = 16-16 = 0.
There is 1 x-intercept at x = -2
The graph is tangent to the x-axis at that point.

Answer 3

a. ax^2=bx=c
>method=b^2-4ac
=4^2+4*1*4
=0
b. there would be onle 1 x-int coz if more than 0, there
would be 2 x-int but less than 0 would show no x-int