The solutions for the quadratic equation are given as follows:
x = -1, x = 7/5
What is a quadratic function?
A quadratic function is given according to the following rule:
y = ax^2 + bx + c
The solutions are:
- [tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex]
- [tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]
In which:
[tex]\Delta = b^2 - 4ac[/tex]
For this problem, the equation is:
5x² - 2x - 7 = 0.
Hence the coefficients are a = 5, b = -2 and c = -7, and then the solutions are found as follows:
- [tex]\Delta = (-2)^2 - 4(5)(7) = 144[/tex]
- [tex]x_1 = \frac{2 + \sqrt{144}}{10} = \frac{7}{5}[/tex]
- [tex]x_2 = \frac{2 - \sqrt{144}}{10} = -1[/tex]
The solutions are:
x = -1, x = 7/5
More can be learned about quadratic equations at https://brainly.com/question/24737967
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