I have an exam coming up, and I am having trouble with a question that is going to be on it. So if anyone could please help, that'd be wonderful
Find a degree 3 polynomial with leading coefficient 4 and zeros -2, 1, and 5.
thanks for any help!
2007-01-15 02:19:28 · 4 answers · asked by Honey 1 in Science & Mathematics ➔ Mathematics
4(x+2)(x-1)(x-5)
Once you multiply this out it will have leading coefficient of 4, and when x=-2 it will be zero (factor of x=2), when x=1 it will be zero (factor of x-1) and when x=5 it will be zero (factor of x-5).
Once you multiply it out (if you have to) you should get
4*x^3-16*x^2-28*x+40
2007-01-15 02:22:20 · answer #1 · answered by a_math_guy 5 · 1⤊ 1⤋
You know the polynomial must have the factorisation
p(x) = c(x + 2)(x - 1)(x - 5),
since these are the roots of p. Also you know c must equal 4, as that is the leading coefficient. So, just multiply the above out, and that is your answer.
2007-01-15 02:26:33 · answer #2 · answered by acafrao341 5 · 1⤊ 1⤋
4x² + ax² + bx + c = 0
x = -2, 1, and 5
Substitute the values and come up with the equations:
4(-8) + a(4) + b(-2) + c = 0
4(1) + a(1) + b(1) + c = 0
4(125) + a(25) + b(5) + c = 0
Now, you have three equations and three variables. Can you solve for these?
2007-01-15 02:25:51 · answer #3 · answered by Dave 6 · 0⤊ 1⤋
4(x+2)(x-1)(x-5)
2007-01-15 02:23:19 · answer #4 · answered by cheerstar114 4 · 1⤊ 0⤋