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Find the largest number $c$ such that the quadratic equation $2x^2+5x+c=x^2+7x$ has at least one real solution.

 Aug 24, 2023
 #1
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2x^2 + 5x + c =  x^2 + 7x    rearrange as

 

x^2 - 2x + c  = 0

 

This will have  at least one  real solution when  the discriminant ≥   0

 

So

 

(-2)^2  - 4(1)(c) ≥ 0

 

4 - 4c ≥  0

 

4 ≥   4c

 

1 ≥ c

 

So....it will have at least one real solution when c ≤ 1

 

cool cool cool

 Aug 24, 2023

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