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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.

 Feb 7, 2024
 #1
avatar+129881 
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x^2 + mx + 4 =  2x^2 + 17x + 8        rearrange as

 

x^2 + (17 - m)x  + 4  =  0

 

If we have two distinct roots, the discriminant > 0  ...... so....

 

(17 - m)^2  - 4(1)(4)  >  0

 

(17 - m)^2  >  16          take the positive root

 

17 - m   >    4

 

13 > m

 

m <  13

 

cool cool cool

 Feb 7, 2024

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