Question

Find the discriminant of the quadratic equation. Determine the number of real solutions. 5x^2 -10x+5=0
What is the discriminant of the quadratic equation?
How many real solutions does the quadratic equation have?
1)two real solutions
2)one real solutions
3)no real solutions

Answer 1

To find the discriminant of the quadratic equation \(5x^2 - 10x + 5 = 0\), we can use the formula for the discriminant, which is given by:

\[
D = b^2 - 4ac
\]

where \(a\), \(b\), and \(c\) are the coefficients of the quadratic equation \(ax^2 + bx + c = 0\).

Here, we have:
- \(a = 5\)
- \(b = -10\)
- \(c = 5\)

Now we can compute the discriminant:

\[
D = (-10)^2 - 4(5)(5)
\]
\[
D = 100 - 100
\]
\[
D = 0
\]

The discriminant \(D = 0\) indicates that the quadratic equation has exactly one real solution.

To summarize:
- The discriminant of the quadratic equation is \(0\).
- The number of real solutions is \(1\).

So the correct answer is:
**2) one real solution**.