Daily Check!!!.

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Presentation transcript:

Daily Check!!!

COMPLEX ROOTS How do I find the x-intercepts of a polynomial equation that will not factor?

COMPLEX ROOTS Quadratic Formula still: Always comes in pairs, conjugate pairs! You will end up with a negative under the radical!! To get rid of the negative, take out an i.

Conjugate Pairs If a + bi is a zero Then a – bi is a zero

Imaginary zeros don’t cross x-axis Imaginary zeros don’t cross x-axis!!!! They are imaginary you can’t see them on a graph.

Find all of the zeros. zeros: x = 0 x = 2i x = -2i Always look to see if a function will factor. This function WILL factor. zeros: x = 0 x = 2i x = -2i

Find all the roots x = -1, 2 f(x) = x4 – 5x3 + 7x2 + 3x - 10 -1 1 -5 7 3 -10 -1 6 -13 10 These are all the roots 2 1 -6 13 -10 2 -8 10 1 -4 5

Find all of the zeros of the function: 5 roots: 3 real 2 imag. BOUNCES! x = -2 x = 1 x = 1

f(x) = (x + 2)(x – 1)(x – 1)(x – 2i)(x + 2i) -2 1 1 2 -12 8 x = 1 -2 4 -10 16 -8 1 1 -2 5 -8 4 1 -1 4 -4 Zeros:: 1 1 -1 4 -4 x = -2 x = 1 1 4 x = 1 x = 2i x = -2i 1 4 f(x) = x2 + 4 Factors: 0 = x2 + 4 f(x) = (x + 2)(x – 1)(x – 1)(x – 2i)(x + 2i) -4 = x2 -2i, 2i = x

#3, 4, &7 Choose any other 3 you want  **Test is next THURSDAY!** Homework!! WS for Homework #3, 4, &7 Choose any other 3 you want  **Test is next THURSDAY!**