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
you need the discriminant to be zero for equal real roots. So,
4-8p = 0
a quadratic with real coefficients cannot have two equal complex roots.
To determine the values of p that make the roots of the quadratic equation equal and non-real, we need to set the discriminant (the expression inside the square root) to zero.
The discriminant of a quadratic equation in the form ax^2 + bx + c = 0 is given by the formula:
Discriminant = b^2 - 4ac
In this case, the quadratic equation is x = (3 ± √(4 - 8p)) / 4. Therefore, our discriminant is:
Discriminant = (4 - 8p) - 4(1)(3)
Discriminant = 4 - 8p - 12
Discriminant = -8p - 8
To find the values of p that make the roots equal and non-real, we need to set the discriminant to zero:
-8p - 8 = 0
Solving for p, we have:
-8p = 8
p = 8/(-8)
p = -1
Therefore, the value of p that makes the roots of the equation equal and non-real is p = -1.