OpenStudy (anonymous):

Find all the zeros of the function and write the polynomial as a product of linear factors: f(x) = x^2 - x + 56

5 years ago
OpenStudy (anonymous):

ax^2 + bx + c format. x = [-b +-sqrt(b^2 - 4ac)] / (2a). The determinant is b^2 - 4ac. If >= 0, then there are real zeros. If not, only complex zeros.

5 years ago
OpenStudy (anonymous):

so i have to put it in quadratic formula?

5 years ago
OpenStudy (anonymous):

or completing the square?

5 years ago
OpenStudy (anonymous):

Short-cut is just to look at the determinant, b^2 - 4ac. If that is <0, you don't have to go further.

5 years ago
OpenStudy (anonymous):

You could complete the square, but that is a little more work.

5 years ago
OpenStudy (anonymous):

pluggin in (1)^2 - 4(1)(56) sor b^2 - 4ac i got -223

5 years ago
OpenStudy (anonymous):

So, no real zeros because you can't have the square root of a negative number. So, cannot be factored (unless you go into the realm of complex numbers).

5 years ago
OpenStudy (anonymous):

tea the aim of this chapter is for complex numbers so im stuck on that

5 years ago
OpenStudy (anonymous):

Then you have to use the full expression for the quadratic formula, x = [-b +-sqrt(b^2 - 4ac)] / (2a).

5 years ago
OpenStudy (anonymous):

is 223 factorable?

5 years ago
OpenStudy (anonymous):

because trying to do the quadratic formula i got stuck on that

5 years ago
OpenStudy (anonymous):

If you want to see if a number is factorable, divide it successively by prime numbers until you use a prime number that when squared is greater than the number you are trying to factor. For instance, when working with 223, you can stop at trying to divide by 17 because 17^2 > 223 and you will have already exhausted all candidates for factoring.

5 years ago
OpenStudy (anonymous):

So, try to factor by 2, 3, 5, 7, 11, 13, and 17.

5 years ago
OpenStudy (anonymous):

|dw:1351354341936:dw|

5 years ago
OpenStudy (anonymous):

To put this into complex number notation, you split the terms and use the relationship of sqrt(ab) = sqrt(a)sqrt(b) where "a" is -1.

5 years ago
OpenStudy (anonymous):

And sqrt(-1) = i.

5 years ago
OpenStudy (anonymous):

|dw:1351355063350:dw|

5 years ago
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