Question

What will be the expression of the polynomial?

Answer 1

SOLUTION

TO DETERMINE

The expression of the polynomial

CONCEPT TO BE IMPLEMENTED

If the Sum of zeroes and Product of the zeroes of a quadratic polynomial is given then the quadratic polynomial is

$\sf{ {x}^{2} -(Sum \: of \: the \: zeroes )x + Product \: of \: the \: zeroes }$

EVALUATION

From the given figure we see that the curve cuts x axis at the point ( - 1,0) & (3,0)

Thus the zeroes of the polynomial are - 1 & 3

Sum of the zeroes

= - 1 + 3

= 2

Product of the zeroes

= - 1 × 3

= - 3

Hence the required Quadratic polynomial

$\sf = {x}^{2} -(Sum \: of \: the \: zeroes )x + Product \: of \: the \: zeroes$

$\sf = {x}^{2} - 2x - 3$

FINAL ANSWER

The expression of the polynomial

$\sf = {x}^{2} - 2x - 3$

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