Quadratic Formula Solver Quadratic Equation is a polynomial equation of second degree. The general form of a quadratic equations is ax2+bx+c = 0. The contributions of the ancient Indian Mathematicians to quadratic equations are quite significant and extensive. Before 800BC Indian Mathematicians constructed 'altars' based on the solutions of quadratic equation ax2+bx+c =0, Aryabhatta gave a rule to sum the geometric series which involves the solution of a quadratic equation. Maximum and Minimum Values of a Quadratic Expression An expression of the type ax2+bx+c is called " quadratic expression". The quadratic expression ax2+bx+c takes different values as x takes different values. Know More About Quadrants of a Graph
As x varies from - to + ax2+bx+c has a minimum value whenever a> 0. The minimum value of the quadratic expression is (4ac-b2 )/4a and it occurs at x = −b2a. 2. has a maximum value whenever a< 0. The maximum value of the quadratic expression is (4ac-b2 )/4a and it occurs at x = −b2a. Quadratic Equation FormulaBack to Top The general form of a quadratic equations is ax2+bx+c = 0 . The set of all solutions of a quadratic equation is called its solution set. The values of x that make a quadratic equation true is called its roots or zeros or solutions. Quadratic equations can be solved by factorization method or by using quadratic formula x = (-b± √(b2-4ac))/(2a) quadratic formula [x = (-b+-sqrt(b] 2 [-4ac))/(2a)] [where b] 2 [ -4ac] [ is called the discriminant of the quadratic equation.] [ A quadratic equation has two roots. ] Learn More On :- Quadrants on a Graph
Rational Expressions Learn about rational expressions concept. Expression is a finite combination of symbols that are well formed and rational expressions is that where the numerator and the denominator or both of them are polynomials. A rational number is a few number that can be printed in the form pq, there are p is specified the integer and q is also specified the integers and q â&#x2030; 0. Rational Expression: If p(x) and q(x) are two polynomials, q(x) 0, then the quotient is called a rational expression. p(x) is known as numerator and q(x) is known as the denominator of the rational expression need not be a polynomial Since a rational number is of the form pq, we can say that a rational expression is also of the form pq, but since it is an expression, it contains variables along with numbers.
Steps to reduce a given rational expression to its lowest terms: Factorize each of the two polynomials p(x) and q(x) Find highest common divisor of p(x) and q(x) If h.c.f. = 1 , then the given rational expression is in its lowest terms If h.c.f 1, then divide the numerator p(x) and denominator q(x) by the h.c.f of p(x) and q(x) The rational expression obtained in Step III or Step IV is in its lowest terms Example :- Reduce the rational expression to its lowest terms Solution :- Let p(x) = x2 -5x-6 = (x-6)(x+1) Let q(x) = x2 + 3x +2 = (x+2)(x+1) Clearly h.c.f of p(x), q(x) = (x+1) (cancel out h.c.f = (x+1))
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