Hello all, i need assistance with these, thanks
1.) Find a cubic function whose graph touches the x-axis at x = -4, passes through the origin and has a value of 10 when x = 5.
2.) The function f(x) = 2x^3 + ax^2 - bx +3. When f(x) is divided by x - 2 the remainder is 15 and f(1) = 0
A.) Calculate the values of a and b
B.) Find the other two factors of f(x)
3.) The polynomial P(x) = x^3 + ax^2 + bx - 9 has zeros at x = 1 and x = -3. The values of a and b are?
Please guys, full working out and answer, me be stupid :P
this isnt homework, its revision so you dont have to worry about me cheating. THANKS!
to A.):
From f(1) = 0 you know that
...... [1]
Use long divison to calculate the remainder. I've got as remainder r = 19 +4a - 2b which is according to your problem 15:
...... [2]
Solve this system of simultaneous equations for a and b. I've got a = 3 and b = 8
Thus the equation of the function becomes:
to B.):
Use synthetic division :
Now solve the quadratic equation
You should get and therefore the other 2 factors are: