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

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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: $P (x) = a (x - α) (x - β) (x - γ), a \neq 0$
Type 2: Two real zeros, one repeated: $P (x) = a (x - α) 2 (x - β), a \neq 0$
Type 3: One real zero repeated three times: $P (x) = a (x - α) 3, a \neq 0$

Type 4: One real and two imaginary zeros: $P (x) = (x - α) (a x 2 + b x + c), △ = b 2 - 4 a c < 0, a \neq 0$
Experiment with the graphs of Type 4 cubics. What is the geometrical significance of $α α$ and the quadratic factor which has imaginary zeros?

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hesgidiauE

Answered 2021-05-06 Author has 106 answers

For the graph of the function $P (x) = (x - α) (a x^{2} + b x + c), △ = b^{2} - 4 a c < 0, a = / 0$
There is only one x-intercept, $(α, 0)$
The other zeros are imaginary.

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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

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