A quadratic polynomial, whose zeros are - 3 and 4, is


- 3 and 4 are the zeroes of the polynomial p(x) = ax2 + bx + c

sum of the zeroes = - (coefficient of x) ÷ coefficient of x2


- 3 + 4 = - b/a


1 = - b/a


b = - 1 and a = 1


Product of the zeroes = constant term ÷ coefficient of x2


c = (- 3)/4


c = 12


Putting the values of a, b and c in the polynomial p(x) = ax2 + bx + c


The polynomial is x2 - x - 12


= x2/2 - x/2 - 6 (dividing by any constant will not change the polynomial)


OR


The equation of a quadratic polynomial is given by x2 - (sum of the zeroes) x + (product of the zeroes) where,


Sum of the zeroes = - (coefficient of x) ÷ coefficient of x2 and


Product of the zeroes = constant term ÷ coefficient of x2


Sum of the zeroes = - 3 + 4 = 1


and


product of the zeroes = (- 3)4 = - 12


x2 - (1)x = (- 12)


= x2 - x - 12


= x2/2 - x/2 - 6


(dividing by any constant will not change the polynomial)

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