Question

Find a quadratic polynomial whose zeroes are 4+√3 and 4-√3

Answer 1

SOLUTION

TO DETERMINE

The quadratic polynomial whose zeroes are

4 +√3 and 4 - √3

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

Here it is given that the zeroes of the quadratic polynomial are 4 +√3 and 4 - √3

Sum of the zeroes

$\sf{ = (4 + \sqrt{3} ) + (4 - \sqrt{3} )}$

$= 8$

Product of the Zeroes

$\sf{ = (4 + \sqrt{3} ) (4 - \sqrt{3} )}$

$\sf{ = {(4)}^{2} - {( \sqrt{3} )}^{2} }$

$= 16 - 3$

$= 13$

Hence the required Quadratic polynomial is

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

$\sf{ = {x}^{2} - 8x + 13}$

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. Out of the following which are proper fractional numbers?

(i)3/2

(ii)2/5

(iii)1/7

(iv)8/3

https://brainly.in/question/4865271

2. the numerator of the fraction is 2 less then denominater. If 3 is added toh both the numerator the fraction becomes 3/4

https://brainly.in/question/30621324

Answer 2

Answer:

Step-by-step explanation:

SOLUTION

TO DETERMINE

The quadratic polynomial whose zeroes are

4 +√3 and 4 - √3

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

EVALUATION

Here it is given that the zeroes of the quadratic polynomial are 4 +√3 and 4 - √3

Sum of the zeroes

Product of the Zeroes

Hence the required Quadratic polynomial is

━━━━━━━━━━━━━━━━