Question

find the quadratic polynomial whose zeros is 2+root3 and 2-root3​

Answer 1

The zeroes of the given equation are a=(2+√3) and b=(2-√3).

now, sum of the roots

a+b= 4

Product of the roots,

ab= 1

Now, the required polynomial is

${x}^{2} - x \times (a + b) + (a \times b) = 0$

Thus, in this case, the polynomial becomes

${x}^{2} - 4x + 1 = 0$

Hope it helps, please mark my answer as brainliest

Answer 2

$\huge\underline\mathfrak\green{Solution}$

The quadratic polynomial of the

(2 + √3) & (2 - √3) is $\</strong><strong>s</strong><strong>m</strong><strong>a</strong><strong>l</strong><strong>l</strong><strong>{\boxed{\bold{</strong><strong>x - 4x + 1</strong><strong>}}}$

$</strong><strong>\</strong><strong>l</strong><strong>a</strong><strong>r</strong><strong>g</strong><strong>e</strong><strong>{\boxed{\bold{</strong><strong>To\</strong><strong>:</strong><strong>find</strong><strong>:</strong><strong>}}}$

"Quadratic polynomial" whose zeros are (2 + √3) & (2 - √3)

$\</strong><strong>l</strong><strong>a</strong><strong>r</strong><strong>g</strong><strong>e</strong><strong>{\boxed{\bold{</strong><strong>S</strong><strong>ol</strong><strong>:}}}$

[x - (2√3)] [x - 2 - (√3)] = 0

= x² - (2 + √3 + 2 - √3) x + (2 + √3) (2 - √3)

= x² - 4x + 1 = 0