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Find the product of all positive integer values of $c$ such that the quadratic equation $3x^2+7x+c=15x-10$ has two real roots.

 Aug 26, 2023
 #1
avatar+128393 
+1

Rearrange as

 

3x^2 -8x + c + 10

 

This will have two real roots when  the  discriminant >   0

 

So

 

(-8)^2  - 4 (3) (c + 10)  >  0

 

64 -120 > 12c

 

-56 > 12c

 

c <  -56 / 12

 

c <  -14/3

 

There are no positive integer  values for c that give two real roots !!!

 

 

cool cool cool

 Aug 27, 2023

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