Question

The quadratic equation x²-4root3x-3=0 has how many roots​

Answer 1

Answer:

2

Step-by-step explanation:

Discrimant is = b²-4ac

Here D= 60>0

So, It has two real roots

Answer 2

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.)