What are the solutions of the polynomial 4x^2-4x+10 4 x 2 − 4 x + 10? write the answer in complex, a+bi a + b i form.

x=+,x=

Answers

a. the are of the rectangle is 18.25

b. 18.25 times two is 36.50

rae me : d

4 packs of water and 7 packs of candy bars

step-by-step explanation:

35x4=140

140/20=7

The solutions of the polynomial are  x=-\frac{1}{2}+\frac{3}{2}i  ,  x=-\frac{1}{2}-\frac{3}{2}i

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 x=\frac{-b(+/-)\sqrt{b^{2}-4ac}}{2a} , where

a is the coefficient of x²b is the coefficient of xc is the numerical term

∵ 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

x=\frac{(-4)(+/-)\sqrt{(-4)^{2}-4(4)(10)}}{2(4)}

x=\frac{-4(+/-)\sqrt{16-160}}{8}

x=\frac{-4(+/-)\sqrt{-144}}{8}

\sqrt{-144}=12\sqrt{-1}

- Substitute  \sqrt{-1}  by i

12\sqrt{-1}=12i

x=\frac{-4(+/-)12i}{8}

- Divide up and down by 4 to simplify the fraction

x=-\frac{1}{2}+\frac{3}{2}i   ,   x=-\frac{1}{2}-\frac{3}{2}i

The solutions of the polynomial are  x=-\frac{1}{2}+\frac{3}{2}i  ,  x=-\frac{1}{2}-\frac{3}{2}i

Learn more:

You can learn more about the quadratic formula in

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