SOLUTION: find the value of p if the equations 3x^2-2x+p=0 and 6x^2-17x+12=0 have a common root.

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Question 940400: find the value of p if the equations 3x^2-2x+p=0 and 6x^2-17x+12=0 have a common root.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

find the value of p if the equations
3x%5E2-2x%2Bp=0 and
6x%5E2-17x%2B12=0
have a common root
find roots:
6x%5E2-17x%2B12=0
6x%5E2-9x-8x%2B12=0
%286x%5E2-8x%29-%289x-12%29=0
2x%283x-4%29-3%283x-4%29=0
%283x-4%29%282x-3%29=0.....roots are
%283x-4%29=0=>3x=4=>highlight%28x=4%2F3%29
and
%282x-3%29=0=>2x=3=>x=3%2F2
3x%5E2-2x%2Bp=0 if x=4%2F3 is same root, then we have
3%284%2F3%29%5E2-2%284%2F3%29%2Bp=0...solve for p
3%2816%2F9%29-2%284%2F3%29%2Bp=0
cross%283%29%2816%2Fcross%289%293%29-%288%2F3%29%2Bp=0
%2816%2F3%29-%288%2F3%29%2Bp=0
8%2F3%2Bp=0
highlight%28p=-%288%2F3%29%29

check the roots using p=-%288%2F3%29
3x%5E2-2x-%288%2F3%29=0...both sides multiply by 3
9x%5E2-6x-8=0......factor
9x%5E2-12x%2B6x-8=0
%289x%5E2-12x%29%2B%286x-8%29=0
3x%283x-4%29%2B2%28x-4%29=0
%283x%2B2%29%283x-4%29=0
roots:
%283x%2B2%29=0=>3x=-2=>x=-2%2F3
and
%283x-4%29=0=>3x=4=>highlight%28x=4%2F3%29 ...which is same as a root of a given equation 6x%5E2-17x%2B12=0
let's see it on a graph: