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

preprekomW

preprekomW

Answered question

2021-06-28

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),Δ=b24ac<0,a0
Experiment with the graphs of Type 1 cubics. Clearly state the effect of changing both the size and sign of a. What is the geometrical significance of α,β,and γ?α,β,and γ?

Answer & Explanation

grbavit

grbavit

Skilled2021-06-29Added 109 answers

The size of ¢ controls the vertical stretch or shrink of the graph Changing the sign of « reflects the graph about x-axis αβ and γ are the x-intercepts of the graph.

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