176k views
3 votes
Y=4x^2−16 has how many real roots?

User Prtitrz
by
8.6k points

1 Answer

3 votes

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.

User Kabilan Mohanraj
by
8.3k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories