SOLUTION: Find two real numbers b such that the expression is a perfect square trinomial. x^2+bx+4/9 I have no idea how to start this problem or I tried to square root the fraction to se

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find two real numbers b such that the expression is a perfect square trinomial. x^2+bx+4/9 I have no idea how to start this problem or I tried to square root the fraction to se      Log On


   

Question 802385: Find two real numbers b such that the expression is a perfect square trinomial.
x^2+bx+4/9
I have no idea how to start this problem or I tried to square root the fraction to see if that would work but it didnt. Please help
Found 2 solutions by solver91311, josmiceli:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


For to be a perfect square, must equal , so for your case:



Solve for the two possible values of

John

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Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
If you wanted to complete the square for
+x%5E2+%2B+b%2Ax+%2B+c+=+0+, you would
subtract +c+ from both sides
+x%5E2+%2B+b%2Ax+=+-+c+
Then you would take 1/2 of the
coefficient of +x+, square it,
and add it to both sides
+x%5E2+%2B+b%2Ax+%2B+%28b%2F2%29%5E2+=+-c+%2B+%28b%2F2%29%5E2+
+x%5E2+%2B+b%2Ax+%2B+b%5E2%2F4+=+-c+%2B+b%5E2%2F4+
The left side is a perfect square trinomial
+%28+x+%2B+b%2F2+%29%5E2+=+-c+%2B+b%5E2%2F4+
----------------------------
Your expression is:
+x%5E2+%2B+bx+%2B+4%2F9+
so, you want
+4%2F9+=+b%5E2%2F4+
+b%5E2+=+16%2F9+
+b+=+sqrt%28+16%2F9+%29+
+b+=+4%2F3+ and also,
+b+=+-4%2F3+
------------
check the answers:
Suppose in my example, +c+=+-5%2F9+
+x%5E2+%2B+b%2Ax+=+-+c+
+x%5E2+%2B+%284%2F3%29%2Ax+=+5%2F9+
Now add +b%5E2%2F4+=+4%2F9+ to both sides
+x%5E2+%2B+%284%2F3%29%2Ax+%2B+4%2F9+=+5%2F9+%2B+4%2F9+
+%28+x+%2B+2%2F3+%29%5E2+=+1+
( the left side is a perfect square )
+x+%2B+2%2F3+=+1+
+x+=+1%2F3+
--------------
And, for +b+=+-4%2F3+,
+x%5E2+-+%284%2F3%29%2Ax+=+5%2F9+
+x%5E2+-+%284%2F3%29%2Ax+%2B+4%2F9+=+5%2F9+%2B+4%2F9+
+x%5E2+-+%284%2F3%29%2Ax+%2B+4%2F9+=+9%2F9+
+%28+x+-+2%2F3+%29%5E2+=+1+
Again, the left side is a perfect square