Question

Form equation whose roots are 5+√3, 5-√3

Answer 1

Answer:

answer is

x*2-10x+25=0

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Answer 2

Answer:

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

Step-by-step explanation:

By using the following formula, we can easily find the quadratic equation:

$\large{\bold{k[x^2 - (\alpha + \beta)x + (\alpha \beta)]}}$

Assumption:

Let $\alpha = 5 + \sqrt{3}$ and let $\beta = 5 - \sqrt{3}$

Now, substituting the values of α and β in the above formula,

$\large{k[x^2 - (5 + \sqrt{3} + 5 - \sqrt{3}) + (5 + \sqrt{3} \times 5 - \sqrt{3})}$

$\large{k[x^2 - 10x + (25 - 3)]}$

[∵ (a + b)(a - b) = a² - b²]

$\therefore \large{k[x^2 - 10x + 22]}$

Substituting k = 1;

∴ The equation is x² - 10x + 22.

∴ The required equation is x² - 10 + 22.