11.2k views
3 votes
What Is The Discriminant For 4r^(2)=8r-1 And What Does It Tell About The Number And Type Of Solutions?

1 Answer

4 votes

The discriminant is a part of the quadratic formula that allows us to determine the nature and number of roots a quadratic equation has. Calculating the discriminant helps to identify how many solutions a quadratic equation has and also assists in determining their type - real or complex.

To find the discriminant, the equation first should be rewritten into its standard form, which is ax^2 + bx + c = 0. Therefore, the equation 4r^2 = 8r - 1 may be rewritten as 4r^2 - 8r + 1 = 0.

In this case, the coefficient a is 4, b is -8 and c is 1.

The formula for the discriminant is D = b^2 - 4ac.

Substituting the relevant values from the equation, we get:

D = (-8)^2 - 4*4*1 = 64 - 16 = 48

Therefore, the discriminant for the given equation is 48.

The discriminant can give us important clues about the roots of the quadratic equation:

- If D > 0, there are two distinct real solutions.
- If D = 0, there's one real root.
- If D < 0, the solutions are complex/imaginary.

Since our calculated discriminant is 48, which is greater than zero, there will be two distinct real solutions for the quadratic equation 4r^2 - 8r + 1 = 0.

User Tom Jonckheere
by
7.9k points

Related questions

1 answer
4 votes
6.0k views
1 answer
5 votes
75.2k views