Question

Find the zeroes of the polynomial p(x) = x2 - 4x +3 and verify the relationship between zeroes and
coefficients.
following quadratic polynomials gaphically:​

Answer 1

Answer:

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

Step-by-step explanation:

Answer 2

Given p(x) = x²-4x+3

= x²-3x-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 and x = 1

Let a = 3 and B = 1

a + B = - b/a

aB = c/ a

Here,

a = 1, b = 4 and c= 3

a+B = 4

aB = 3