SOLUTION: If one of the zero of the quadratic polynomial f(x) = 3x2 – 20x + 3p + 4 is four times the other, find the value of p.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: If one of the zero of the quadratic polynomial f(x) = 3x2 – 20x + 3p + 4 is four times the other, find the value of p.       Log On


   

Question 1032132: If one of the zero of the quadratic polynomial f(x) = 3x2 – 20x + 3p + 4 is four times the other, find the value of p.

Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Let 3x%5E2+-+20x+%2B3p+%2B+4++=+0.
==> x%5E2+-+%2820%2F3%29x+%2B+%283p+%2B+4%29%2F3++=+0.
Now if one root is a, then by hypothesis, the other root is 4a.
==> -%28a%2B4a%29+=+-20%2F3, and a%284a%29+=+4a%5E2+=+%283p+%2B+4%29%2F3.
==> a+=+4%2F3, and 4%2816%2F9%29+=+%283p+%2B+4%29%2F3.
==> 64%2F9+=+%283p+%2B+4%29%2F3. ==> p+=+52%2F9