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math in hl HELP

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astarmathsandphysics:
Few mins

astarmathsandphysics:

Write 5A2-6A=3I in the form AB=I and hence find A-1 in terms of A and I
5A^2-6A+1=4I so (A-I)(5A-!)=4I so A-1= 4I(5A-1)^-1

IGSTUDENT:
Need help in a few questions:

1)The polynomial p(x) + (ax+b)3 leaves a remainder of -1 when divided by x+1 and a remainder of 27 when divided by x-2.Find the values of the real numbers a and b.

2)Given that the roots of the equation x3-9x2 +bx -216 =0 are consecutive terms in a geometric sequence find the value of b and solve the equation.

astarmathsandphysics:
1)x+1=0 so x=-1 p(-1)=(-a+b)^3 =-1 so -a+b=-1 (1)
x-2=0 so x=2 p(2)=(2a+b)=3 so 2a+b=3 (2)
(2)-(1) 3a=4 so a=4/3
b=a+1 =7/3

I did the other one already somewhere - I will try to find a link

astarmathsandphysics:
The orrts are anyway 1,6,36

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