Answer:
2 real roots
Explanation:
- We can determine how many roots a quadratic has by using the discriminant, which is b^2 - 4ac, which comes from the quadratic formula.
- b, a and c are also seen in the standard form of a quadratic and its general equation is given by:
y = ax^2 + bx + c
- For 4x^2 - 16, 4 is our a value, 0 is our b value, and -16 is our c value.
- When the discriminant is less than 0, there are no real roots.
- When the discriminant equals 0, there is 1 real root.
- When the discriminant is greater than 0, there are 2 real roots.
Thus, we can plug in 4 for a, 0 for b, and -16 for c to determine how many real roots y = 4x^2 - 16 has:
0^2 - 4(4)(-16)
(-16)(-16)
256
256 > 0
Since 256 is greater than 0, there are 2 real roots for y = 4x^2 - 16.