# How would you use the discriminant to find all values, lets say of c which the equation has two real solutions? Equation: 2x²-x-c=0

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given Equation is 2x^2 -x -c = 0

comapre this equation with the quadratic equation ax^2+bx+c = 0,

such that a=2 , b= -1 and c= -c

As the equation has two real roots its discriminant b^2 - 4ac = 0

plug in a,b,c in b^2 - 4ac = 0, and solve for c

we get , (-1)^2 - 4*2* (-c) = 0

1 - 8*(-c) = 0

1+8c = 0

8c = -1

such that c = -1/8

thus the constant in 2x^2 -x-c = 0 is c= -1/8

`2x²-x-c=0`

`a=2` `b=-1` `c=-c ` the formula to find the discriminant is `b^2-4ac` plug it in

`-1^2-4(2)(-c)` simplify

`1+8c` make an equation and solve

`1+8c=0`

`8c=-1`

`(8c)/8= (-1)/8`

`c= -1/8`