Question

If the zeroes of a quadratic polynomial are 5+√3 and 5-√3 then the quadratic polynomial is​

Answer 1

Answer:

Step-by-step explanation:

let 5+$\sqrt{3$ be ∝  

      and 5-$\sqrt{3$ be β

 therefore the required quadratic equation is = x²-(∝+β)x + ∝β

                                                   =x²-(5+√3 + 5-√3 )x+( 5-√3)(5+√3)

                                                    = x²-10x +(25-9)

                                                      = x²- 10x +16

therefore the required quadratic equation is x²-10x+16

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

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