Question

. Find the number of real number solutions for the equation. x2 − 2x + 9 = 0

Answer 1

Your answer would be, There is No Real Solution to the equation.

Use the discriminant to solve for number of real roots.

Use the Quadratic Formula: a = 1, b =  - 2,  c = 9


D = b^2 - 4ac
Y = ax^2 + bx + c

D = ( - 2)^2  - 4 * 1 * 9
             4      -    36
=               -  32

Since the discriminant is a negative, Therefore, there is  No Real Solution to the Equation.

Answer 2

Answer:

x = 1 + $\frac{\sqrt{32} }{2}$i   or     1 -$\frac{\sqrt{32} }{2}$i , therefore no real number solution.

Step-by-step explanation:

x² - 2x + 9 = 0

We are going to use formula method to find the solution to the equation below

x = -b ± √ b² - 4ac  / 2a

From the equation given;

a = 1   b=-2  and c = 9

We can now proceed to insert the values into the formula;

x = -b ± √ b² - 4ac  / 2a

x = 2  ± √ -2² - 4(1)(9)  /   2(1)

x = 2 ± √ 4 - 36  / 2

x  =  2 ±√ -32    / 2

x = $\frac{2}{2}$ ± $\frac{\sqrt{-32} }{2}$

x = 1 ± $\frac{\sqrt{32} }{2} \sqrt{-1}$

x = 1 ±$\frac{\sqrt{32} }{2}$i

Either  x = 1 + $\frac{\sqrt{32} }{2}$i   or     1 -$\frac{\sqrt{32} }{2}$i

Therefore no real number solutions to the equation