Q. 144.0( 4 Votes )

Find the zeroes o

Answer :

To find the zeros of the polynomial let us first solve the polynomial by equating it to zero. Factorizing the given polynomial

2x2 – 8x + 6 = 0


To factorize the polynomial we have,


Sum of the value should be equal = -8


Product should be equal to = 2 × 6


= 12


So two numbers are -2, -6


2x2 – 2x – 6x + 6 = 0


2x(x – 1) – 6(x – 1) = 0


(2x-6)(x – 1) = 0


2x-6 = 0 or x-1 = 0


Solving first part,


2x-6 = 0


2x = 6


x = 3


Solving second part,


x – 1 = 0


x = 1


When we compare the above quadratic equation with the generalized one we get,


ax2 + bx + c = 0


a = 2, b = -8, c = 6


Sum of zeroes = -b / a


= - (-8) / 2


= 4


Product of zeroes = c / a


= 6 / 2


= 3


Zeroes obtained are 3 and 1 and their sum is 4 and product is 3 which is matching to the answer obtained through the ratio of coefficients.


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