Question

Write the polynomial whose zeroes are (5 + V3) and (5 - V3).​

Answer 1

The polynomial is

The polynomial is ${x}^{2} - 10x + 22$

Given:

Zeroes of a polynomial are (5+√3). and (5-√3)

To find:

The polynomial.

Solution:

We know that the polynomial whose zeroes are given is

${x}^{2} + - (\alpha + \beta )x + \alpha \beta$

where,

$\alpha \: and \: \beta \: are \: zeroes \: of \: polynomial$

Sum of zeroes= 5+√3+5-√3

=10

Product of zeroes= (5+√3)(5-√3)

Using property,

=25-3

=22

So the polynomial is

So the polynomial is${x}^{2} - 10x + 22$

#SPJ3

Answer 2

Answer:

The polynomial is $x^{2} - 10x+22$

Explanation:

We have been given that the zeroes of a polynomial are $(5+\sqrt{3} )$ and $(5 - \sqrt{3} )$.

We have to find the polynomial.

Step By Step Solution:

We can write the polynomial as,

$x^{2} +-(\alpha +\beta )x+\alpha \beta$

where,

$\alpha$ and $\beta$ are the zeroes of this polynomial.

The sum of the zeroes given is,

$5+\sqrt{3} +5-\sqrt{3} =10$

The product of the zeroes given is,

$(5+\sqrt{3} )(5-\sqrt{3} ) = 25 - 3 = 22$

Now, substituting these values in the equation of the polynomial we get,

$x^{2} -10x+22$

Hence, the polynomial whose zeroes are $(5+\sqrt{3} )$ and $(5-\sqrt{3} )$ is $x^{2} -10x+22$

#SPJ2