Question

if alpha and beta are the zeroes of a polynomial x2-4√3x+3,then find the value of alpha +beta -alpha beta​

Answer 1

Answer:

answer is 4root3-3

Step-by-step explanation:

Answer 2

Answer:

The value of α + β - αβ is  4√3 - 3

Step-by-step explanation:

Given Quadratic polynomial : x² - 4√3x + 3  and α & β are zeroes of the given polynomial.

To find: α + β - αβ

First we solve the given polynomial to find zeroes.

x² - 4√3x + 3 = 0

using quadratic formula,

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$x=\frac{-(-4\sqrt{3})\pm\sqrt{(-4\sqrt{3})^2-4\times3}}{2}$

$x=\frac{4\sqrt{3}\pm\sqrt{48-12}}{2}$

$x=\frac{4\sqrt{3}\pm6}{2}$

$x=2\sqrt{3}\pm3$

So, α = 2√3 + 3   and β = 2√3 - 3

also, αβ = ( 2√3 + 3 )( 2√3 - 3 ) = (2√3)² - (3)² = 12 - 9 = 3

Thus,

α + β - αβ = ( 2√3 + 3 ) + ( 2√3 - 3 ) - ( 3 ) = 4√3 - 3

Therefore, The value of α + β - αβ is  4√3 - 3