![]() To do that, we would set our factors equal to zero and solve. Well, factoring the quadratic equation then sets us up to be able to find out where exactly our roots are, and our roots just mean where our graph is equal to zero. Well, if you recall a quadratic equation is always a parabola (or U-shaped graph). ![]() Maybe you’re asking, why on earth do I even need to factor? Why can’t I just leave it as it is? \(x^2\) and \(x\) share a common factor of \(x\). But, we still have something that can be factored out. Now, we have \(8(x^2 + 2x)\) being multiplied by everything on the inside. So, we can go ahead and factor out that 8. Well, 8 and 16 share a common factor of 8. What are the common factors of \(8x^2 + 16x = 0\)? Say we have the equation \(8x^2 + 16x = 0\) The easiest way to do this is to find the common factor. Now, expanding can be pretty easy we know exactly what to do to expand them when given our factors, but figuring out how to factor our expanded version can be a little harder. So, again we have our factors \((x + 2)(x + 6)\) on the left, and when you multiply that you get the expanded version: \((x^2+ 8x + 12)\). Once you multiply together you get \(x^2+ 8x + 12\). The actual quadratic equation is the expanded, or multiplied out version, of your two factors that are being multiplied.įor example, \((x + 2)\) and \((x + 6)\) are my factors that are being multiplied together. Suppose we have two variables ‘x’ and ‘y’.In order to factor a quadratic, you just need to find what you would multiply by in order to get the quadratic. ![]() You have to solve both of the Quadratic equations to get to know the relation between both variables. Generally, two quadratic equations in two different variables are given. Questions on Quadratic Equations are asked in the form of inequalities in the Quantitative Aptitude section. Understanding the pattern of Quadratic Equations asked in bank examsīank exams often include these types of Quadratic Equation questions to assess candidates' problem-solving skills and their ability to discern relationships between variables, making it a critical component of the quantitative section. Completing the square or square root method.Using quadratic formula or Shridharacharya formula.Quadratic equations can be factorized through various methods such as So, the roots of the equation 2x 2 - 7x + 3 = 0 are x1 = 3 and x2 = 1/2.įactoring quadratics is a technique used to represent the quadratic equation ax^2 + bx + c = 0 as a multiplication of its linear factors in the form (x - p) (x - q), where p and q represent the roots of the quadratic equation ax^2 + bx + c = 0. Now, substitute the values into the quadratic formula: Solve using Quadratic formula 2x 2 - 7x + 3 = 0Ĭomparing the equation with the general form ax 2 + bx + c = 0 gives, The Quadratic Formula is a rule that says that, in any equation of the form ax2 + bx + c = 0, the solution x-values of the equation are given by: In cases where certain quadratic equations resist easy factorization, the Quadratic formula offers a convenient and efficient means to swiftly calculate the roots. The Quadratic formula stands as the most straightforward method for determining the roots of a quadratic equation. This particular form, ax 2 + bx + c = 0, where 'a' is not equal to zero, is referred to as the standard form of a quadratic equation.Īlso known as the Sridharacharya formula, the quadratic formula is a formula that provides the two solutions to a quadratic equation. However, to establish the standard representation of this equation, we arrange the terms of p(x) in descending order of their degrees, resulting in ax 2 + bx + c = 0, with a ≠ 0. ![]() For instance, 2x 2 + x - 300 = 0 is a quadratic equation. Smartkeeda offers a diverse range of Quadratic Equation questions with solutions to facilitate effective practice and enhance your prospects of achieving a high score.Ī quadratic equation, denoted by the variable x, takes the form of ax 2 + bx + c = 0, where a, b, and c represent real numbers, with a ≠ 0. Nonetheless, with dedicated practice, you can attain mastery and achieve a perfect score in this area. Achieving proficiency in this topic demands keen observational skills. You can expect a set of 5 questions on this topic in the prelims of every banking and insurance examination. Quadratic equation is one of the most important and potentially high-scoring topics asked in different banking and insurance exams, such as IBPS PO, SBI PO, SBI Clerk, IBPS Clerk, RRB Assistant, RRB Scale 1, LIC Assistant, LIC AAO, etc.
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