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Let $m$ be a real number. If the quadratic equation $x^2+mx+4 = 2x^2 + 17x + 8$ has two distinct real roots, then what are the possible values of $m$? Express your answer in interval notation.

 Jun 21, 2024
 #1
avatar+129725 
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Simplify as

 

x^2 + (17 - m)x + 4  = 0

 

If we have two distinct roots  then the discriminant is > 0

 

So

 

(17- m)^2 - 4*4  >  0

 

(17 - m)^2  > 16      take both roots

 

17  - m  > 4           17 - m <  -4

 

 13 > m                  21 < m

 

m  comes  from (-inf , 13) U ( 21, inf)

 

cool cool cool

 Jun 21, 2024

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