![]() Replace x by (x-4) in the above equation. Construct a quadratic equation from x 2 7x 16 = 0 The required equation can be obtained by substituting ky in place of x in the given equation.ġ. V) A quadratic equation (say in y) whose roots are 1/ k times the roots of the equation ax 2 bx c=0, i.e. The required equation can be obtained by substituting y/k in place of x in the given equation Iv) A quadratic equation (say in y) whose roots are k times the roots of the equation ax 2 bx c=0, i.e. The required equation can be obtained by substituting (y k) in place of x in the given equation. the roots are (α – k) and (β – k) or x-k=y Iii) A quadratic equation (say in y) whose roots are k less than the roots of the equation ax 2 bx c=0, i.e. The required equation can be obtained by substituting (y-k) in place of x in the given equation. the roots are (α k) and (β k) or x k=y Ii) A quadratic equation (say in y) whose roots are k more than the roots of the equation ax 2 bx c=0, i.e. we get the equation required by interchanging the co-efficient of x 2 and the constant term. ![]() This can be obtain by substituting 1/x in place of x in the given equation giving us cx 2 bx a =0, i.e. the roots of the required equation are 1/α and 1/β. I) A quadratic equation whose roots are the reciprocals of the roots of the given equation ax 2 bx c=0 i.e. If we are given a quadratic equation, we can obtain a new quadratic equation by changing the roots of this equation in the manner specified to us. For this condition, we shall consider 5 possible relations. If p is the sum of the roots of the quadratic equation and q is the product of the roots of the quadratic equation, then the equation can be written as x 2 – px q = 0Ĭ. If the roots of the quadratic equation are given as α and β, the equation can be written as: The relation between the roots of the equation to be obtained and the roots of another equation is given.Ī.The sum of the roots and the products of the roots of the quadratic equation are given.The roots of the quadratic equation are given.The following conditions occur frequently. Very often we are required to obtain a quadratic equation when some conditions are given. #Roots of quadratic equation how to#It would be a waste of time to explain how to find roots to a CAT aspirant so skipping the very normal basics let’s understand the various types of question on quadratic that appears in CAT exam. Discriminant (D or Δ) or determinant just determines the nature of roots of a quadratic equation.Home » Blog » How to Construct a Quadratic Equation Based on Given Conditions in the CAT? How to Construct a Quadratic Equation Based on Given Conditions in the CAT?Īs we all know a quadratic equation is a second-degree polynomial in x equated to zero and also if the co-efficient of x 2 is zero, it becomes a linear equation. The only relation which establishes between equal roots of two different quadratic equations are :ĭifference of two roots of a quadratic equation is : sqrt(D)/a which is not equal to D. X 2 - (Sum of two roots)x (Product of two roots) = 0 So we can also write a quadratic equation in this form :Ī quadratic equation is written in this form : Let x and y be the two distinct roots of quadratic equation ax 2 bx c = 0Īnd D = b 2-4ac then xy (Product of two roots)= c/a and x y (Sum of two roots) = -b/a. ![]() The first corresponds to the case when you have repeated roots (obviously) and the second occurs when a^2b^2 - 4a^3c - 1 = 0. I'm not sure what your asking here, but the quadratic discriminant is \Delta = b^2 - 4ac. ![]()
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