Algebra 2 Help with Homework: x2 + 5x + 9 = 0

x2 + 5x + 9 = 0
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I will assume you mean: \(\displaystyle \L x^{2} + 5x + 9 = 0\)

This cannot be easily factored, so you will need to complete the square to solve for the two roots. Note: There are no real zeros for this function. You will have two complex roots in the form a+bi

Why is this? This is because with the rigid transformation (vertical shift) from the leading coefficient of 9, moves your parabola up enough so that it does not intercept the x axis.
 
Hint: (2k)^2 - (2k - 2)^2 = 52

Not enough? See your teacher.
 
morson said:
jwpaine said:
You will have two complex roots in the form a+bi
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Isn't that always the case with quadratics?
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No.

Your two solutions will be in the complex form a+bi if there are no x-intercepts. The solutions in this case would involve a square root of a negative number.

The discriminate b^2 - 4ac =[ 5^2 - 4(1)(9) ] = -11 which tells us that there are no real solutions to this quadratic.

Cheers,
John.
 
The real numbers are a subset of the complex numbers. Every real number can be expressed in the form "a + bi" where b = 0. So, in fact, it is correct to say that every quadratic equation has two complex solutions. In some cases, those complex solutions are also real.
 
I'm sorry. I didn't mean to give false information.

I'm learning too :)
 
Yes....and the more you learn about math, the more you will come to see that there is LOTS more to learn. Keep at it!
 
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