ATAR Notes: Forum

VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: tolga on December 23, 2009, 11:19:20 pm

Title: polynomial equations
Post by: tolga on December 23, 2009, 11:19:20 pm: 1)find a and b, if P(x)=ax^6+bx^4+x^3-6,3P(1)=-24 and 3P(-2)=102
2)The functions y=x^3-2x^2+ax+10 and y=6+(a+b)x-4x^2-x^3 both have (-1,0) as an x-intercept. Find the values of a and b>
Title: Re: polynomial equations
Post by: TrueTears on December 23, 2009, 11:22:51 pm: 1. $3(a+b-5) = -24 \cdots [2]$

$6(32a+8b-7) = 102 \cdots [1]$

Solve simultaneously.
Title: Re: polynomial equations
Post by: tolga on December 23, 2009, 11:28:00 pm: shouldn't the second equation be -6 because 3times-2
Title: Re: polynomial equations
Post by: TrueTears on December 23, 2009, 11:29:44 pm: Quote from: tolga on December 23, 2009, 11:28:00 pm
shouldn't the second equation be -6 because 3times-2
Nope, just sub in $-2$ for $x$ and multiply by 3.
Title: Re: polynomial equations
Post by: tolga on December 23, 2009, 11:34:01 pm: yeah then why isn't the second equation start with 3 but 6 if it 3P(-2) doesn't it mean sub -2 and 3(the whole equation)
Title: Re: polynomial equations
Post by: TrueTears on December 23, 2009, 11:37:00 pm: Quote from: tolga on December 23, 2009, 11:34:01 pm
yeah then why isn't the second equation start with 3 but 6 if it 3P(-2) doesn't it mean sub -2 and 3(the whole equation)
No just -2 :)

3 is multiplying the entire polynomial :P
Title: Re: polynomial equations
Post by: tolga on December 23, 2009, 11:43:30 pm: yeah i get that but for [1] it starts with 6 instead of 3 cause it's 3P9-2)