The polynomial p(x)is given by p(x)=ax3 +16x2+cx – 120, where a and c are constants. The three zeros of p(x)are –2, 3 and α. Find the value of α.
with working out please
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By the remainder and factor theorems, if is a root then .
So you should find:
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After you have simplified these, you have 2 equations in 2 unknowns. Solve them simultaneously for and .
Once you have and , you have the polynomial.
Since is a root, is a factor.
Since is a root, is a factor.
Long divide your polynomials by these factors to find the third factor. From there you can find the final root .
If you have any more trouble, please show your working and exactly where you are stuck.
ok is this right um i subbed -2 and 3 into the equations
and got -8a+64-2c-120=0(1) and 27a+144+3c-120=0(2)
then i did -8a+64-2c-120(times by -3) and 27a+144+3c-120(times by 2)
which is 24a+6c+168=0(3) and 54a+6c+44=0(4)
then i did (4)-(3)
which is 30a-124=0
30a=124
a=124 divide by 30
=4.13
sub a=4.13 into (4)
can you tell me if this is right so far.