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IGSTUDENT:
I have 3 question in maths,

1. Given that the roots of the equation x^3-9x^2+bx-216=0 are consecutive terms in a geometric sequence, find the value of b and solve the equation

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

3. Prove that when a polynomial p(x) is divided by ax-b the remainder if p(b/a)

Thanks

astarmathsandphysics:
1.It must factorise as (x-a)(x-b)(x-c) with a b and c all integers
Multiply this to givex^3-x^2(ab+bc+ac)+x(a+b+c)-216 (1)
If the smallest root is t then the other roots are rt and r^2t so product of roots r^3t^3=216
rt=6 so r=1,t=6 or r=6,t=1 or r=2,t=3 or some variation of these with plus or minus too.
I think a typo x^3-90x^2+bx-216=0 I get (x+3)(x+6)(x-12) b=-3
2.(-a+b)^3=-1 so -a+b=-1
(2a+b)^3=27 so 2a+b=3
a=4/3 b=1/3
will have to wait for q3

IGSTUDENT:
thanks!!!

IGSTUDENT:
Some more doubts...

1. Consider the trigonometric curve y=sin(2x-pi/2)
a) Find dy/dx and d2y/dx2

2. Find an equation for a line that is tangent to the graph of y=e^x that passes through the origin

3. Find the derivatice of y with repect to x, dy/dx by implicity differentiation: xy(x+y)^1/2=1

4. Find the derivative of y with repect to x, dy/dx: ln(1+x^2)^1/2=xarctanx

Thanks!

astarmathsandphysics:
One mo

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