Algebra
Basic formula for Algebra
Systems of EquationsThere are two systems of equations:1) Consistent System. 2) Inconsistent System. A system of equations involving two or more simultaneous linear equations, is consistent in nature if it has atleast one solution. A system of equations involving two or more simultaneous linear equations, is inconsistent in nature if it has no solution. Let us consider two linear equations  Unique Solution i.e. lines intersect  Infinitely Many Solution i.e lines overlap  No Solution i.e lines coincide  Quadratic EquationsPractice form of a quadratic equation is ax2 + bx + c = 0, where a, b,c are real numbers and a ≠ 0. Quadratic equation is a polynomial equation of second degree. Fundamental Theorm of Algebra ensures that it has two solutions. These solutions can be real or complex. is known as the Quadratic Formula.Sum of the roots = -b/a Product of the roots = c/a D = b2 - 4ac is known as the discriminant. Value of 'D' helps us to identify the nature of roots. 1) If D > 0 then the quadratic equation has real and unequal roots. 2) If D = 0 then the quadratic equation has real and equal roots. Value of equal roots is given by  3) If D < 0 then the quadratic equation has complex roots. If 'S' is the sum of the roots of the quadratic equation and 'P' is the product of the roots of the quadratic equation then the equation is given as x2 - Sx + P = 0 |