We are given a quadratic equation, and we are asked to find the discriminant.
The quadratic equation we're given is 1-2a^2=7a-2. To match the general form of the quadratic equation (ax^2 + bx + c = 0) and facilitate our calculations, let's first rewrite this equation. After rearranging, we get -2a^2 + 7a - 1 = 0.
From this equation, we can see that:
a = -2, b = 7, c = -1
To find the discriminant, we use the formula for the discriminant of a quadratic equation, which is b^2 - 4ac.
So, substituting the values of a, b, and c in the formula, we get:
discriminant = 7^2 - 4*(-2)*(-1)
After performing the operations, we find that the discriminant equals 41.
Thus, the discriminant of the given quadratic equation is 41.
We can use the value of the discriminant to understand the nature of the roots of the quadratic equation. Since the discriminant is positive, the quadratic equation has two distinct real roots.