FIND THE ZEROES OF THE QUADRATIC POLYNOMIAL AND VERIFY THE RELATIONSHIP BETWEEN THE ZEROES AND COFFICIENT OF POLYNOMIAL
In the general form of quadratic polynomial ax2 + bx + c, there are two zeros say α and β, then; Sum of the zeros = α + β = -b/a = -(coefficient of x) / (coefficient of x2), and Product of zeros = α.β = c/a = (Constant Term) / (Coefficient of x2) Example: Find the zeros of the quadratic polynomial x2 + 7x +10, and verify the relationship between the zeroes and the coefficients. We have, x2 + 7x +10 = (x +2) (x+5) So, the value of x2 + 7x + 10 is zero, when x+2 = 0 or x+5 = 0, i.e., when, x = -2 or x = -5. Therefore, the zeroes of x2 + 7x + 10 are -2 and -5. Now, the relationship between zeros and coefficient of above polynomial can be shown as:- Sum of zeroes = -2 + (-5) = -7 = -(7)/1 = -(coefficient of x) / (coefficient of x2) Product of zeroes = (-2) x (-5) = 10 =10/1 = (constant Term) / (coefficient of x2Example on Relationship Betrween Zeros and Coefficient of a Polynomial