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

1 answer

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.