Every cubic polynomial can be categorised into one of four types: Type 1: Three real, distinct zeros: P(x)=a(x−α)(x−β)(x−γ),a≠0 Type 2: Two real zeros

Tyra 2021-05-05 Answered

Every cubic polynomial can be categorised into one of four types: Type 1: Three real, distinct zeros: P(x)=a(xα)(xβ)(xγ),a0
Type 2: Two real zeros, one repeated: P(x)=a(xα)2(xβ),a0
Type 3: One real zero repeated three times: P(x)=a(xα)3,a0

Type 4: One real and two imaginary zeros: P(x)=(xα)(ax2+bx+c),=b24ac<0,a0
Experiment with the graphs of Type 4 cubics. What is the geometrical significance of αα and the quadratic factor which has imaginary zeros?

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Expert Answer

hesgidiauE
Answered 2021-05-06 Author has 106 answers

For the graph of the function P(x)=(xα)(ax2+bx+c),=b24ac<0,a=/0
There is only one x-intercept, (α,0)
The other zeros are imaginary.

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