Question

Suppose that f(x, y)=e⁻³ x²- 1 y²+3 x+4y then find the discriminant of f.

Answer 1

The discriminant of the given function f(x, y) = e^(-3x^2 - y^2 + 3x + 4y) is -3.

Step-by-step explanation:

The discriminant of a quadratic function is the expression under the square root sign in the quadratic formula. In this case, the function is f(x, y) = e^(-3x^2 - y^2 + 3x + 4y). To find the discriminant of f, we need to write the function in the form ax^2 + bx + c and then calculate the discriminant, which is b^2 - 4ac.

First, we rearrange the function to e^(-3x^2 + 3x - y^2 + 4y) = 0. Now we can identify a, b, and c:

• a = -3
• b = 3
• c = -1

Plugging these values into the discriminant formula, we get the discriminant of f as (-3)^2 - 4(-3)(-1) = 9 - 12 = -3.