Question

The zeroes of a quadratic polynomial p(x) are 3 + √5 and 3 - √5. Which polynomial represents the quadratic polynomial p(x) ?

Answer 1

Answer:

Step-by-step explanation:

The roots are 3 + √5 and 3 - √5.

Sum of roots = 3 + √5 + 3 - √5 = 6

Product of roots = 3 + √5  * 3 - √5 = 9 - 5 = 4.

The polynomial is of form x² + (Sum of roots)x + Product of roots = 0

=> x² + 6x + 4 = 0    

Answer 2

The quadratic polynomial whose zeroes are,

$5 \sqrt{3} ,5 - \sqrt{3}$

$\alpha , \beta \: is \: f(x) = k[ {x}^{2} - ( \alpha + \beta )x + \alpha \times \beta ]$

where k is any non-zero real no.

THE QUADRATIC POLY POLYNOMIAL WHOSE ZEROES ARE

$5 \sqrt{3} ,5 - \sqrt{3}$

$f(x) = k[ {x}^{2} - ( \alpha + \beta )x + \alpha \times \beta ]$

$f(x) = k[ {x}^{2} - ( 5 \cancel{ + \sqrt{3}} + 5 \cancel{ - \sqrt{3}} )x + (5 + \sqrt{3} ) (5 - \sqrt{3} ) ]$

$f(x) = k[ {x}^{2} -10x + ( {5)}^{2} - ({ \sqrt{3} )}^{2} ]$

$f(x) = k[ {x}^{2} -10x + (25 - 3)]$

$f(x) = k[ {x}^{2} -10x + 22]$

so, the QUADRATIC polynomial is

$f(x) = k[ {x}^{2} -10x + 22]$