Solving polynomials: find bounds on zeroes; find polynomial

[deedie_06]

1.Find the integer-valued upper and lower bounds to the zeros of the polynomial function f(x)=6x^4-7x^3-26x^2+7x+20.

2. Find the polynomial of degree 3 with the real coefficients that satifies the given condition zeros: 3,i,-i; P(2)=0.

 

[stapel]

What have you tried? Where are you stuck?

1) You've applied the Rational Roots Test and... then what?

2) You've converted from "x = a" (zero) form to "x - a" (factor) form, multiplied the factors, and... then what?

Please be complete and specific. Thank you.

Eliz.

 

[morson]

For the second question, I do not think that a polynomial satisfies those conditions. Or I'm just too sleepy.

You have told us that there are 4 zeros to a cubic (and by the fundamental theorem of algebra, we know there are only 3 complex zeros).

 

[stapel]

You have told us that there are 4 zeros to a cubic...

Good catch! I only noticed that another point was provided, which would allow the poster to solve for "a" in "a(x - b)(x - c)(x - d)".

But since that point is actually a fourth zero for a polynomial which can have only three, there must be something wrong with the exercise.

Eliz.