Question

Write a quadratic polynomial the sum of whose zeroes is -3 and product is -10.​

Answer 1

Answer:

the quadratic polynomial is :- x+y =-3

x×y=-10

Answer 2

The required quadratic polynomial whose sum of whose zeroes is - 3 and product is - 10 is x² + 3x - 10

Given :

For a polynomial sum of whose zeroes is - 3 and product is - 10

To find :

The quadratic polynomial

Concept :

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

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

Solution :

Step 1 of 2 :

Find Sum of zeroes and Product of the zeroes

Here it is given for a polynomial sum of whose zeroes is - 3 and product is - 10

Sum of zeroes = - 3

Product of the zeroes = - 10

Step 2 of 2 :

Find the quadratic polynomial

The required quadratic polynomial

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

$\displaystyle \sf = {x}^{2} - (-3)x + (-10)$

$\displaystyle \sf{ = {x}^{2} + 3x - 10 }$

Hence the quadratic polynomial whose sum of whose zeroes is - 3 and product is - 10 is x² + 3x - 10

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