Use the discriminant to determine whether the following equations have solutions that are: two different rational solutions; two different irrational solutions; exactly one rational solution; or two different imaginary solutions.8x2 + 2x + 4 = 0
Only one equation is given.
. Use the discriminant to determine whether the following equations have solutions that are: two different rational solutions; two different irrational solutions; exactly one rational solution; or two different imaginary solutions.
8x2 + 2x + 4 = 0
Two different irrational solutions
Two different imaginary solutions
Exactly one rational solution
Two different rational solutions
which one
two different rational solutions
To determine the type of solutions for the quadratic equation 8x^2 + 2x + 4 = 0, we can use the discriminant. The discriminant is a value calculated from the coefficients of a quadratic equation and is found using the formula: b^2 - 4ac.
For the equation 8x^2 + 2x + 4 = 0, the coefficients are:
a = 8
b = 2
c = 4
Plugging these values into the formula, we get:
Discriminant = b^2 - 4ac = (2)^2 - 4(8)(4)
Calculating further:
= 4 - 128
= -124
The discriminant is -124.
Now, using the value of the discriminant, we can determine the type of solutions:
1. If the discriminant is greater than 0 (positive), then the equation has two different real solutions.
2. If the discriminant is equal to 0 (zero), then the equation has exactly one real solution.
3. If the discriminant is less than 0 (negative), then the equation has two different imaginary solutions.
In this case, since the discriminant (-124) is negative, the equation 8x^2 + 2x + 4 = 0 has two different imaginary solutions.