For the graph of the function \(P(x)=(x-\alpha)(ax^2+bx+c), \triangle=b^2-4ac<0, a=/0\)

There is only one x-intercept, \((\alpha, 0)\)

The other zeros are imaginary.

asked 2021-06-28

Type 2: Two real zeros, one repeated: \(\displaystyle{P}{\left({x}\right)}={a}{\left({x}−α\right)}{2}{\left({x}−β\right)},{a}≠{0}\)

Type 3: One real zero repeated three times: \(\displaystyle{P}{\left({x}\right)}={a}{\left({x}−α\right)}{3},{a}≠{0}\)

Type 4: One real and two imaginary zeros: \(\displaystyle{P}{\left({x}\right)}={\left({x}−α\right)}{\left({a}{x}{2}+{b}{x}+{c}\right)},Δ={b}{2}−{4}{a}{c}{<}{0},{a}≠{0}\)

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 \(\alpha, \beta, and\ \gamma ? \alpha,\beta,and\ \gamma\)?

asked 2021-05-30

Type 2: Two real zeros, one repeated: \(P(x)=a(x-\alpha)2(x-\beta),a \neq 0\)

Type 3: One real zero repeated three times: \(P(x)=a(x-\alpha)3,a \neq 0\)

Type 4: One real and two imaginary zeros: \(P(x)=(x-\alpha)(ax2+bx+c),\triangle=b2−4ac<0,a \neq 0\)

Experiment with the graphs of Type 4 cubics. What is the geometrical significance of \(\alpha \alpha\) and the quadratic factor which has imaginary zeros?

asked 2021-06-05

Type 2: Two real zeros, one repeated: \(P(x)=a(x-\alpha)2(x−\beta),a \neq 0\)

Type 3: One real zero repeated three times: \(P(x)=a(x- \alpha)3,a\neq0\)

Type 4: One real and two imaginary zeros: \(P(x)=(x-\alpha)(ax2+bx+c),\triangle=b2−4ac<0,a \neq 0\)

Experiment with the graphs of Type 4 cubics. What is the geometrical significance of \(\alpha \alpha\); and the quadratic factor which has imaginary zeros?

asked 2020-12-06

asked 2021-06-08

asked 2021-06-20

asked 2021-05-23