Question

find a quadratic polynomial with zeros 3+√2 and 3-√2. in full method

Answer 1

Hello !!

Here is the answer.

Given two zeroes = 3+√2 and 3-√2.

Sum of zeroes = 3+ √2 + 3 -√2 = 6,
Product Of Zeroes = (3+ √2)(3 - √2) = 9-2 = 7. [Using (a+b)(a-b) = a² - b²]

Now, Using Basic Quadratic Equation :

p(x) = kx² - (sum of zeroes) x + (product of zeroes)
p (x) = x² - 6x + 7

Hope You Got It

Answer 2

$\alpha = 3 + \sqrt{2} \: \: \: \: \: \beta = 3 - \sqrt{2}$
$\alpha + \beta = 6 \: \: \: \: \alpha \beta = 9 - 2 = 7$
general formula of quadratic equation
${x}^{2} - ( \alpha + \beta )x + \alpha \beta = 0$
${x}^{2} - 6x + 7 = 0$
this is the required quadratic equation