The solutions of the polynomial are [tex]x=-\frac{1}{2}+\frac{3}{2}i[/tex] , [tex]x=-\frac{1}{2}-\frac{3}{2}i[/tex]
Step-by-step explanation:
The solutions of a polynomial is the value of x when the polynomial equal to zero
The formula of quadratic polynomial is [tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}}{2a}[/tex] , where
∵ The polynomial is 4x² - 4x + 10
- Equate it by zero to find its solutions
∴ 4x² - 4x + 10 = 0
∵ The coefficient of x² is 4
∴ a = 4
∵ The coefficient of x is -4
∴ b = -4
∵ The numerical term is 10
∴ c = 10
- Use the formula to find the values of x
∵ [tex]x=\frac{(-4)(+/-)\sqrt{(-4)^{2}-4(4)(10)}}{2(4)}[/tex]
∴ [tex]x=\frac{-4(+/-)\sqrt{16-160}}{8}[/tex]
∴ [tex]x=\frac{-4(+/-)\sqrt{-144}}{8}[/tex]
∵ [tex]\sqrt{-144}=12\sqrt{-1}[/tex]
- Substitute [tex]\sqrt{-1}[/tex] by i
∴ [tex]12\sqrt{-1}=12i[/tex]
∴ [tex]x=\frac{-4(+/-)12i}{8}[/tex]
- Divide up and down by 4 to simplify the fraction
∴ [tex]x=-\frac{1}{2}+\frac{3}{2}i[/tex] , [tex]x=-\frac{1}{2}-\frac{3}{2}i[/tex]
The solutions of the polynomial are [tex]x=-\frac{1}{2}+\frac{3}{2}i[/tex] , [tex]x=-\frac{1}{2}-\frac{3}{2}i[/tex]
Learn more:
You can learn more about the quadratic formula in brainly.com/question/8196933
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