Question

Construct a quadratic equation whose roots are root 2 and 2 root
2​

Answer 1

Step-by-step explanation:

Let

$\alpha = \sqrt{2} \: and \: \beta = 2 \sqrt{2}$

$we \: know \: formula \:$

${x}^{2} - ( \alpha + \beta )x + \alpha \beta = 0$

ok so let's find

$\alpha + \beta = 2 \sqrt{2} + \sqrt{2}$

$and$

$\alpha \beta = 4$

So put this in equation=>

${x}^{2} - (2 \sqrt{2} + \sqrt{2} )x + 4 = 0$

$hope \: it \: helps \: you \: buddy$

Answer 2

The quadratic equation is  $x^2-3\sqrt{2} x+4= 0$

Step-by-step explanation:

To find: A quadratic equation whose zeroes are √2 and 2√2

Now as we know quadratic equation is given by

$x^2-(\alpha +\beta)x+\alpha \beta=0$ where $\alpha$ and $\beta$ are the roots of quadratic equation

Therefore

$\alpha = \sqrt{2} \\\\\beta =2\sqrt{2}$

So

$\alpha +\beta = \sqrt{2} +2\sqrt{2} =3\sqrt{2} \\\\ \alpha \beta = \sqrt{2} \times 2\sqrt{2} = 4$

Hence, the quadratic equation will be $x^2-3\sqrt{2} x+4= 0$

#Learn more

Find a quadratic polynomial whose zeros are 3+√5/5 and 3-√5/5.​

brainly.in/question/16182170