Question

if alpha and beta are the two zero of the polynomial x square minus 4 root 3 X + 3 find the value of alpha + beta minus alpha beta

Answer 1

Method of Solution:


Equation : x²+4√3x+3

For the Zeroes of Polynomial f(x)= (x²+4√3x+3)

Zeroes of Polynomial = -b/a -(Coefficient of x)/Coefficient of x²


Sum of Zeroes of Polynomial = -4/√2 ÷1 => -4/√2

Sum of Zeroes = -4/√2

Product of Zeroes of Polynomial = C/a =(Constant term)/Coefficient of x²

[ Product of Zeroes = 3/1 => 1 ]

Therefore, We have obtained (a+ß ) = 4/√2

(aß) = 3


According to the Question Statement!

Statement: find the value of alpha + beta - alpha beta

Substitute the obtained value,

alpha + beta - alpha beta

(4/√2) - (1)

=>
$\frac{4}{ \sqrt{2} } - 1 \\ \\ \frac{4 - \sqrt{2} }{ \sqrt{2} }$