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

x = 1 +
`(√(32) )/(2)`i or 1 -
`(√(32) )/(2)`i , therefore no real number solution.

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 =
`(2)/(2)` ±
`(√(-32) )/(2)`

x = 1 ±
`(√(32) )/(2) √(-1)`

x = 1 ±
`(√(32) )/(2)`i

Either x = 1 +
`(√(32) )/(2)`i or 1 -
`(√(32) )/(2)`i

Therefore no real number solutions to the equation