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For what real values of $a$ is $x^2 + ax + 25$ the square of a binomial? If you find more than one, then list your values in increasing order, separated by commas.

 Apr 22, 2018
 #1
avatar+98005 
+1

x^2  + ax  +  25

 

Just like an earlier problem, set the discriminant to 0 and solve for a

 

So we have

 

a^2   -  4(1)(25)  = 0

 

a^2  - 100  = 0     factor this

 

(a - 10) (a + 10)  = 0

 

Setting both factors to 0 and solving for a  gives a  = 10   or a  = -10

 

So

 

a  = -10, 10

 

 

cool cool cool

 Apr 22, 2018

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