Question

Find the quadratic polynomial whose Sun and product of zeroes are √3 and 1/2

Answer 1

Answer:

please refer to image attached

Answer 2

Let the zeroes be alpha and beta

→ Sum of zeroes

$\alpha + \beta = \sqrt{3}$

→ Product of zeroes

$\alpha \beta = \frac{1}{2}$

The required quadratic polynomial would be

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

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

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

Let's consider k = 2

[Note : k can be any number, I'm considering it to be 2 as to cancel the denominator]

$\boxed{answer : 2 {x}^{2} - 2 \sqrt{3} x + 1}$

Hope this helps, I hope this isn't confusing though ^^"

Have a good evening!