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If (ax + b)(bx + a) = 6x^2 + __ x + 6, where a, b and __ are distinct integers, what is the minumum possible value of __ , the coefficient of x?

 

\(\phantom{26x^2, 26}\)

 

\(\phantom{8x^2, 8}\)

 Jun 30, 2022

Best Answer 

 #1
avatar+2293 
+1

We know that \(ab = 6\), meaning the pairs of \((a,b)\) are (1,6), (2,3) (3,2), (6,1)

 

The coefficient of x will be \(b^2x + a^2x\)

 

Now, just try out the pairs, and find the least possible value.

 Jun 30, 2022
 #1
avatar+2293 
+1
Best Answer

We know that \(ab = 6\), meaning the pairs of \((a,b)\) are (1,6), (2,3) (3,2), (6,1)

 

The coefficient of x will be \(b^2x + a^2x\)

 

Now, just try out the pairs, and find the least possible value.

BuilderBoi Jun 30, 2022

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