Question

solve the question in the attachment ​

Answer 1

Answer:

If alpha and beta are the zeroes of polynomial x²-4√3x+3 then find value of alpha+beta-alpha×beta?

Polynomial in variable x :

p(x)=x2−4 3–√x+3

Given,

α,β are the zeroes of p(x) .

p(x) is a quadratic polynomial with a degree 2

From the properties of a quadratic polynomial, we know the relation between quotients (those constants except for variables) and zeroes — α,β .

In p(x) , a=1|b=−43–√|c=3

sum of Zeroes:-

α+β=−ba→

−(−43√)1

43–√

α+β=43–√ ——————— Eq.1

Product of Zeroes :-

αβ=ca

31

αβ=3 —————Eq.2

(α+β)−(αβ)=?

43–√−3

(α+β)−(αβ)=43–√− 3≈(4×1.732)−3

≈6.92−3

≈3.92

∴(α+β)−(αβ)=43–√−3≈3.92 (approx.)

:)

So let the polynomial be p(x)

now as per the conditions

alpha +beta = -b/a

therefore on comparing coefficients we get 4root3 as the value of alpha +beta

for the product of zeroes the condition is

alpha.beta=c/a

therefore the product of alpha and beta is 3

putting the above values in

alpha +beta - alpha. beta

we get

4root3 -3

Answer 2

SOLUTION:-

If alpha and beta are the zeroes of

polynomial x-4V3xt+3 then find value of

alphatbeta-alphaxbeta?

Polynomial in variable x:

Px-x2-4 3-Vx+3

Given,

a,ß are the zeroes of px).

px) is a quadratic polynomial with a degree

2

From the properties of a quadratic

polynomial, we know the relation between

quotients (those constants except for

variables) and zeroes a,ß.

In pX), a=1lb=-43-Vlc=3