The solutions of the quadratic equation 0 = -3x² - 4x + 5 are
[tex]x=\frac{-2-\sqrt{19}}{3}[/tex] and [tex]x=\frac{-2+\sqrt{19}}{3}[/tex]
Step-by-step explanation:
The quadratic formula of the quadratic equation ax² + bx + c = 0, is
[tex]x=\frac{-b+-\sqrt{b^{2}-4ac}}{2a}[/tex]
To find the solution of the quadratic equation by using quadratic formula
- Find the values of a, b, and c from the quadratic equation
- Substitute these values in the quadratic formula
- Calculate the values of x
∵ -3x² - 4x + 5 = 0
∴ a = -3 , b = -4 and c = 5
- Substitute these values in the quadratic formula
∵ [tex]x=\frac{-(-4)+\sqrt{(-4)^{2}-4(-3)(5)}}{2(-3)}[/tex]
∴ [tex]x=\frac{4+\sqrt{16+60}}{-6}[/tex]
∴ [tex]x=\frac{4+2\sqrt{19}}{-6}[/tex]
- Simplify by dividing up and down by -2
∴ [tex]x=\frac{-2-\sqrt{19}}{3}[/tex]
∵ [tex]x=\frac{-(-4)-\sqrt{(-4)^{2}-4(-3)(5)}}{2(-3)}[/tex]
∴ [tex]x=\frac{4-\sqrt{16+60}}{-6}[/tex]
∴ [tex]x=\frac{4-2\sqrt{19}}{-6}[/tex]
- Simplify by dividing up and down by -2
∴ [tex]x=\frac{-2+\sqrt{19}}{3}[/tex]
The solutions of the quadratic equation 0 = -3x² - 4x + 5 are
[tex]x=\frac{-2-\sqrt{19}}{3}[/tex] and [tex]x=\frac{-2+\sqrt{19}}{3}[/tex]
Learn more:
You can learn more about quadratic equation in brainly.com/question/7361044
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