SOLUTION: Show that the given values of c are zeros of P (x), and find all other zeros of P (x). P (x) = 2x^4 - 5x^3 - 24x^2 - 7^x + 10; c = 1/2, -2 Thank you for the homework help!

Algebra ->  Equations -> SOLUTION: Show that the given values of c are zeros of P (x), and find all other zeros of P (x). P (x) = 2x^4 - 5x^3 - 24x^2 - 7^x + 10; c = 1/2, -2 Thank you for the homework help!      Log On


   

Question 199449: Show that the given values of c are zeros of P (x), and find all other zeros of P (x).
P (x) = 2x^4 - 5x^3 - 24x^2 - 7^x + 10; c = 1/2, -2
Thank you for the homework help!
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
I assume you meant 2x%5E4+-+5x%5E3+-+24x%5E2+-+7x+%2B+10
You are told two roots are -2 and 1/2
First use this URL --> http://www.calc101.com/webMathematica/long-divide.jsp#topdoit
Divide the given polynomial by x%2B2 since x%2B2 as a factor means -2 is a solution.
That yields a result with no remainder. So, x-2 is in fact a root.
Now take the result from this division and divide that by x+-+1%2F2
That also divides without a remainder. Take the quotient of that division, which is a quadratic, and solve it using the methods you have already learned. (factoring, quadratic equation, etc)