Question

Find the quadratic polynomial, the sum and product of whose zeroes

are 6 and 9 respectively. Hence find the zeroes.​

Answer 1

Given :-

• Sum of zeroes = 6

• Product of zeroes = 9

To Find :-

• The quadratic polynomial

Solution :-

Formula used :

→ x² + ( sum of zeroes )x + product of zeroes

→ x² ( 6 )x + 9

→ x² + 6x + 9

Quadratic polynomial is x² + 6x + 9

Answer 2

Step-by-step explanation:

Given the sum is six and product is 9 let the quadratic equation be of unknown term x.

We write the quadratic equation as follows since none of the digits is negative :

x^2 + 6x + 9 = 0

The above is the quadratic equation.

We can now solve for x as follows :

The digits when multiplied gives 9 and when added gives 6 is 3 and 3.

x^2 + 3x + 3x + 9 = 0

Collecting like terms together :

x(x + 3) + 3(x + 3) = 0

(x + 3)(x + 3) = 0

X = - 3

The roots are - 3 and - 3

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