A quadratic equation is a mathematical expression in the form of ax² + bx + c = 0, where a, b, and c are constants and x is the variable. It is a polynomial equation of degree 2, and its graph forms a parabola.
To find the integral values of 'k' for 2 rational solutions, we first need to set the quadratic equation equal to 0. Then, we can use the quadratic formula: x = (-b ± √(b²-4ac)) / 2a. The value of 'k' will be the constant 'a' in this formula. We can then solve for 'k' by plugging in the known values for 'a', 'b', and 'c'.
Having 2 rational solutions in a quadratic equation means that the graph of the equation will intersect the x-axis at 2 distinct points. This also means that the equation can be factored into 2 linear expressions, making it easier to solve.
No, a quadratic equation can have at most 2 rational solutions. This is because a quadratic equation is a polynomial equation of degree 2, and according to the Fundamental Theorem of Algebra, a polynomial of degree n can have at most n complex solutions. Since rational numbers are a subset of complex numbers, this means that a quadratic equation can have at most 2 rational solutions.
If a quadratic equation has no rational solutions, it means that the graph of the equation does not intersect the x-axis, or in other words, it has no real roots. This can happen if the discriminant (b²-4ac) is negative, or if the equation cannot be factored into 2 linear expressions with rational coefficients.