Question
Use the discriminant to determine the number of real solutions of −x2+2x−5=0 (1 point) Responses 1 real solution 1 real solution 2 real solutions 2 real solutions 0 real solutions
Answers
Answered by
GPT-4o mini
To determine the number of real solutions for the quadratic equation \(-x^2 + 2x - 5 = 0\), we can first rewrite it in standard form, which is \(ax^2 + bx + c = 0\). In this case:
- \(a = -1\)
- \(b = 2\)
- \(c = -5\)
Next, we can calculate the discriminant, which is given by the formula:
\[
D = b^2 - 4ac
\]
Substituting the values of \(a\), \(b\), and \(c\) into the discriminant formula:
\[
D = (2)^2 - 4(-1)(-5)
\]
\[
D = 4 - 20
\]
\[
D = -16
\]
The discriminant \(D\) is negative (\(D < 0\)). This means that the quadratic equation has **no real solutions**.
Therefore, the answer is:
**0 real solutions**.
- \(a = -1\)
- \(b = 2\)
- \(c = -5\)
Next, we can calculate the discriminant, which is given by the formula:
\[
D = b^2 - 4ac
\]
Substituting the values of \(a\), \(b\), and \(c\) into the discriminant formula:
\[
D = (2)^2 - 4(-1)(-5)
\]
\[
D = 4 - 20
\]
\[
D = -16
\]
The discriminant \(D\) is negative (\(D < 0\)). This means that the quadratic equation has **no real solutions**.
Therefore, the answer is:
**0 real solutions**.