The solution to a quadratic equation is x is equals to 3 plus or minus square root of 4 minus 8p all over 4 where p is the element of Q.

Determine the value(s) of p that the roots of the equation are equal and non-real

see related questions below.

polynomials with real coefficients cannot have equal complex roots.

To determine the values of p for which the roots of the quadratic equation are equal and non-real, we need to set the discriminant (the part inside the square root) to zero.

The discriminant formula for a quadratic equation of the form ax^2 + bx + c = 0 is given by:
Discriminant (D) = b^2 - 4ac

In this case, we have the quadratic equation in the form x = (3 ± √(4 - 8p))/4. Therefore, a = 1, b = -3, and c = -1.

Now, let's set the discriminant equal to zero and solve for p:
D = (4 - 8p) - 4(-1)(1)
0 = 4 - 8p + 4
8p = 8
p = 1

So, the value of p for which the roots of the equation are equal and non-real is p = 1.