Homework Check.

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Presentation transcript:

Homework Check

Daily Check!!! (Irrational Roots)

3B.5 – 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 discriminant! (value 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.

Ex 1. Find all of the zeros. zeros: x = 0 x = 3i x = -3i Always look to see if a function will factor. This function WILL factor. zeros: x = 0 x = 3i x = -3i

Ex 2. 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

Ex 3. Find all of the zeros of the function: -2 1 1 2 -12 8 -2 4 -10 16 -8 1 1 -2 5 -8 4 1 -1 4 -4 1 -1 4 -4 Zeros: x = -2 x = 1 x = 1 x2 + 4=0 x – 1 =0 x = 2i x = -2i X2 =-4 x = 1 x = -2i, 2i

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

Ex 4. Find all the solutions: f(x) = 7x3 -18x2 + 20x - 24 2 7 -18 20 -24 14 -8 24 7 -4 12

Finding Polynomials Distribute Repeat as necessary Look out for radicals and complex/imaginary roots.

Finding Polynomials

Homework!!