Question

find the quadratic polynomial whose zeroes are - 2 upon root 3 and root 3 upon 4

Answer 1

in attachment the question is solved

Answer 2

Answer:

Required polynomial is $k(4\sqrt{3}x^2+5x-2\sqrt{3})$

Step-by-step explanation:

Given: Zeroes of quadratic polynomial is $\frac{-2}{\sqrt{3}}\:and\:\frac{\sqrt{3}}{4}$

let α and β are the zeroes of the polynomial.

First we find sum of zeroes and product of zeroes.

Sum of zeroes, α + β = $\frac{-2}{\sqrt{3}}+\frac{\sqrt{3}}{4}=\frac{-8+3}{4\sqrt{3}}=\frac{-5}{4\sqrt{3}}$

Product of zeroes, αβ = $\frac{-2}{\sqrt{3}}\times\frac{\sqrt{3}}{4}=\frac{-2\sqrt{3}}{4\sqrt{3}}=\frac{-1}{2}$

So, the polynomial is

k ( x² - ( α + β )x + αβ )

$=k(x^2-\frac{-5}{4\sqrt{3}}x+(\frac{-1}{2}))$

$=k(x^2+\frac{5}{4\sqrt{3}}x-\frac{-2\sqrt{3}}{4\sqrt{3}})$

$=k(4\sqrt{3}x^2+5x-2\sqrt{3})$

Therefore, Required polynomial is $k(4\sqrt{3}x^2+5x-2\sqrt{3})$