Using the quadratic formula, the solutions are:
a) [tex]x = \frac{3 \pm \sqrt{41}}{4}[/tex]
b) [tex]x = 1 \pm 2i[/tex]
What is a quadratic function?
A quadratic function is given according to the following rule:
[tex]y = ax^2 + bx + c[/tex]
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]
Item a:
The coefficients are a = 2, b = -3, c = -4, hence:
- [tex]\Delta = (-3)^2 - 4(2)(-4) = 41[/tex]
- [tex]x_1 = \frac{3 + \sqrt{41}}{4}[/tex]
- [tex]x_2 = \frac{3 - \sqrt{41}}{4}[/tex]
Item b:
The coefficients are a = 1, b = 2, c = 2, hence:
- [tex]\Delta = (2)^2 - 4(1)(2) = -4[/tex]
- [tex]x_1 = \frac{2 + \sqrt{-4}}{2} = 1 + 2i[/tex]
- [tex]x_2 = \frac{2 - \sqrt{-4}}{2} = 1 - 2i[/tex]
More can be learned about quadratic equations at https://brainly.com/question/24737967
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