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

- 3 and 4 are the zeroes of the polynomial p(x) = ax^{2} + bx + c

∴ sum of the zeroes = - (coefficient of x) ÷ coefficient of x^{2}

- 3 + 4 = - b/a

1 = - b/a

b = - 1 and a = 1

Product of the zeroes = constant term ÷ coefficient of x^{2}

c = (- 3)/4

⇒ c = 12

Putting the values of a, b and c in the polynomial p(x) = ax^{2} + bx + c

∴ The polynomial is x^{2} - x - 12

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

OR

The equation of a quadratic polynomial is given by x^{2} - (sum of the zeroes) x + (product of the zeroes) where,

Sum of the zeroes = - (coefficient of x) ÷ coefficient of x^{2} and

Product of the zeroes = constant term ÷ coefficient of x^{2}

∴ Sum of the zeroes = - 3 + 4 = 1

and

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

⇒ x^{2} - (1)x = (- 12)

= x^{2} - x - 12

= x^{2}/2 - x/2 - 6

(dividing by any constant will not change the polynomial)

5