Question

Find the polynomial whose zeroes 5+√19and5-√19

Answer 1

i think the ans is

${x}^{2} + 10x + 6$

or

${ \times }^{2} - 10x + 6$

Answer 2

The required polynomial is

$p(x) = x^2 - 10x + 6$

Step-by-step explanation:

We are given the following in the question:

The two zeroes of a polynomial are:

$\alpha = 5 + \sqrt{19}, \beta = 5 - \sqrt{19}$

Sum of roots:

$\alpha + \beta = 5 + \sqrt{19} + 5 - \sqrt{19} \\\alpha + \beta = 10$

Product of roots is:

$\apha \beta = (5 + \sqrt{19})(5-\sqrt{19}) = 25 - 19\\\apha \beta = 6$

The polynomial can be written as:

$x^2 - (\alpha + \beta )x + \alpha \beta\\x^2 - (10)x + 6\\p(x) = x^2 - 10x + 6$

is the required polynomial.

#LearnMore

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