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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.

 Jan 11, 2024
 #1
avatar+128732 
+1

Simplify as

 

x^2 + (17 - m)x + 4  >  0

 

If two distinct roots,the discrminant  >  0

 

So

 

(17 - m)^2  -  4(1)(4)   >  0

 

(17 - m)^2  >  16           take  both roots

 

17 - m > 4                   17   - m  <  -4 

 

17 - 4 > m                    21 < m               

 

m < 13                         m >  21

 

m = ( -inf , 13) U ( 21, inf)

 

 

cool cool cool

 Jan 11, 2024

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