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Can anyone help?

 

Find the product of all positive integer values of $c$ such that $8x^2+15x+c=7x^2-20x+8$ has two real roots.

 Apr 11, 2022
 #1
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8x^2 + 15x + c =  7x^2 -20x + 8           rearrange as

 

x^2 + 35x + (c - 8)   = 0

 

To have two real roots, the discriminant must be > 0

 

So

 

35^2  - 4(1) (c - 8)  >  0

 

1225 - 4c + 32  >  0

 

1257  - 4c > 0

 

1257 > 4c

 

4c < 1257

 

c < 1257 / 4  =  314.5

 

So...any integer  c < 314.5  will work

 

And since c must be a positive integer  c =  1 * 2 * 3 * 4 * .....* 312 * 313 * 314

 

So....the product of  all integer c's  =  314!      [ a really BIG number !!!!!]

 

 

cool cool cool 

 Apr 11, 2022
edited by CPhill  Apr 11, 2022

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