for given two quadratic equations how to find which equation has larger or smaller or equal roots compared to other without finding its roots for banks examsthe normal methods are time consuming
We'll check the coefficients of the given quadratics.
We could write a quadratic equation when we know the sum and the product of the roots, as it follows:
x^2 - Sx + P = 0
S = x1 + x2 and P = x1*x2
Comparing the given quadratics with this form, we can easily identify the sums and the products of the roots, such as, later on, we can compare their roots.
x^2 - 6x + 5 = 0
x^2 -4x + 3 = 0
We notice that the sum and the product of the 1st quadratic are: S1 = 6 and P1 = 5, therefore x1 = 1 and x2 = 5.
We notice that the sum and the product of the 2nd quadratic are: S2 = 4 and P2 = 3, therefore x1 = 1 and x2 = 3.
We can conclude that two roots are equal and the 2nd root of the 1st equation is larger than the 2nd root of the 2nd equation.
Therefore, identifying the sum and the product of the roots, we can compare the roots of different quadratics.