Question

Find a quadratic polynomial whose zeros are 4 +root 5 and 4 - root 5

Answer 1

heya☺

Quadratic polynomial ---

x^2 - ( Sum of zeroes )x + Product of zeroes

x^2 - ( 4+√5 + 4-√5 ) x + {( 4+√5)( 4-√5)}

x^2 - 8x + 16 - 5
x^2 -8x +11

✌✌ Hope this helps !

Answer 2

Answer:

$\text{The required polynomial is }x^2-8x+11$

Step-by-step explanation:

Given the zeroes of quadratic polynomial we have to find the polynomial.

$\text{The zeroes are }4+\sqrt5\text{ and }4-\sqrt5$

The sum of zeroes are

$4+\sqrt5+(4-\sqrt5)=4+4=8$

Product of zeroes are

$(4+\sqrt5).(4-\sqrt5)=16-(\sqrt5)^2=16-5=11$

The quadratic polynomial is

$x^2-(\text{sum of zeroes})x+(\text{product of zeroes})$

$x^2-8x+11$

$\text{The required polynomial is }x^2-8x+11$