The general form of a linear equation in two unknowns x and y is ax + by + c = 0 where a and b are non-zero coefficients. Two equations a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 form a pair of simultaneous equations in x and y. A value for each unknown which satisfies both equations at the same time gives the roots / solution of the equation.
An equation in the form ax2 + bx + c = 0, where x is a variable and a, b and c are constants with a ≠ 0 is called a quadratic equation. When b = 0 the equation is called a pure quadratic equation and when b ≠ 0 the equation is called an affected quadratic.
b2 – 4ac is known as the discriminant in the equation as it discriminates the nature of roots of the equation
If b2 – 4ac = 0, the roots are real and equal If b2 – 4ac > 0, the roots are real and distinct (unequal) If b2 – 4ac < 0, the roots are imaginary If b2 – 4ac is a perfect square the roots are real rational and distinct If b2 – 4ac > 0 but not a perfect square the roots are real irrational and distinct