Question

find the zeroes of the polynomial p(x) = x^2 - 4x + 3 and verify the relationship between zeroes and coefficients.​

Answer 1

Given, p(x)=x
2
−4x+3
=x
2
−3x−x+3
=x(x−3)−1(x−3)
=(x−3)(x−1)

For zeroes of polynomial, p(x)=0
i.e. (x−3)(x−1)=0
or, x=3 or x=1

Let, α=3 and β=1
α+β=
a
−b
​

αβ=
a
c
​


Here, a=1b=−4c=3
α+β=4
αβ=3



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