SOLUTION: Let the roots of the equation 3x2 -(p-4)x-(2p+1)=0 be alpha and beta. find the quadratic equation whose roots are apha+2 and beta+2

Algebra ->  Algebra  -> Polynomials-and-rational-expressions -> SOLUTION: Let the roots of the equation 3x2 -(p-4)x-(2p+1)=0 be alpha and beta. find the quadratic equation whose roots are apha+2 and beta+2      Log On

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Question 9228: Let the roots of the equation 3x2 -(p-4)x-(2p+1)=0 be alpha and beta. find the quadratic equation whose roots are apha+2 and beta+2
Answer by khwang(438) About Me  (Show Source):
You can put this solution on YOUR website!
You should type the equation as 3x^2 -(p-4)x-(2p+1)=0
which is equivalent to x^2 -(p-4)/3 x-(2p+1)/3=0
since alpha ,beta are two roots,from the relationship of roots and
coeffieicnts,we have

alpha + beta = (p-4)/3 and
alpha * beta = -(2p+1)/3
to find the required equation, we have to get the
sum and product of alpha+ 2 and beta + 2

Now, alpha+ 2 + beta + 2 = (p-4)/3 + 4 = (p+8)/3
and their product as
(alpha+ 2) * (beta + 2 )
= alpha * beta + 2(alpha + beta )+ 4
= -(2p+1)/3 + 2(p-4)/3 + 4
= -9/3 + 4
= 1
So,the solution equation is
x^2 -(p+8)/3 x + 1 = 0
or equivalently
3x^2 -(p+8) x + 3 = 0

If you have trouble understanding the details, try to think carefully.
I may not supply further explanations.
Kenny