To determine the number of real number solutions for the quadratic equation \(x^2 + 9x + 20 = 0\), we can use the discriminant method.
The general form of a quadratic equation is \(ax^2 + bx + c = 0\).
For \(x^2 + 9x + 20 = 0\), the coefficients are:
- \(a = 1\)
- \(b = 9\)
- \(c = 20\)
The discriminant \(\Delta\) of a quadratic equation \(ax^2 + bx + c = 0\) is given by:
\[
\Delta = b^2 - 4ac
\]
Substituting the given values:
\[
\Delta = 9^2 - 4(1)(20) = 81 - 80 = 1
\]
The discriminant \(\Delta = 1\), which is greater than 0.
The nature of the roots depends on the value of the discriminant:
- If \(\Delta > 0\), there are 2 distinct real roots.
- If \(\Delta = 0\), there is 1 real root (a repeated root).
- If \(\Delta < 0\), there are no real roots (the roots are complex).
Since \(\Delta = 1 > 0\), the equation \(x^2 + 9x + 20 = 0\) has 2 distinct real number solutions.
Therefore, the correct answer is:
2
5.
Find the number of real number solutions for the equation.
x2 + 9x + 20 = 0
1
0
2
1 answer