Question

Find a quadratic polynomial whose sum and product of zeroes are
$\sqrt{2}$ and $\frac{1}{3}$ respectively.

Answer 1

Hey✨

The sum of zeroes are

$\sqrt{2}$

And the product of zeroes are

$\frac{1}{3}$

Let the one zero =

$\alpha$

And the second zero =

$\beta$

Now we know that,

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

${x}^{2} +( \sqrt{2} )x - \frac{1}{3}$

${x}^{2} + \sqrt{2} x - \frac{1}{3}$

Multilplying the whole equation by 3, we'll get:

$3 {x}^{2} + 3\sqrt{2} x + 3$