A quadratic form is a function of the form: $$Q(x) = a_0x^2 + 2a_1x + a_2$$ where \(a_0, a_1, a_2\) are constants. This function represents a plane in \(R^2\) w...
A quadratic form is a function of the form:
where (a_0, a_1, a_2) are constants.
This function represents a plane in (R^2) with the equation in the general form of (Ax^2 + Bx + C = 0) where (A, B, C) are constants.
The coefficients (a_0, a_1, a_2) are called the coefficients of the quadratic form.
The roots of the quadratic form are the solutions to the equation (a_0x^2 + a_1x + a_2 = 0).
A quadratic form is said to be positive definite if the value of (a_0) is positive, a negative definite if (a_0) is negative, and a positive semi-definite if (a_0) is positive and (a_1^2 - 4a_0 a_2 > 0)