Question

Express the quadratic polynomial with the zeros 3+√5 and 3–√5​

Answer 1

Answer:

Step-by-step explanation:

Here 3+√5=alpha(A)

And 3-√5=beta(B)

Now,sum of the roots =(3+√5)+(3-√5)

=9-3√5+3√5-5

=4

Product of roots=(3+√5)(3-√5)

=(3)^2-(√5)^2

=4

The equation will be

X^2-x(sum of roots)+(product of roots)

= X^2-4x+4. Is the equation

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

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