Question

Use the discriminant to determine how many solutions are possible for the following equation?(show work)

5x -3x+4-0. I know there are_______
real solutions to the equation in problem 4 because______.
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Answer 1

see the explanation

Explanation:

The correct question is

Use the discriminant to determine how many solutions are possible for the following equation (show work).

5x^2-3x+4=0

we know that

The discriminant for a quadratic equation of the form

`ax^(2) +bx+c=0`

is equal to

`D=b^2-4ac`

If D=0 then the equation has only one real solution

If D>0 then the equation has two real solutions

If D<0 then the equation has no real solutions (two complex solutions)

in this problem we have

`5x^(2) -3x+4=0`

so

`a=5\\b=-3\\c=4`

substitute

`D=-3^2-4(5)(4)`

`D=-71`

so

The equation has no real solutions, The equation has two complex solutions

therefore

I know there are___No____

real solutions to the equation in problem 4 because ___the discriminant is negative___