Question

find the zeroes of x^2-4x+3 and verify relation to coefficient in the polynomial​

Answer 1

Answer:

p(x)=x²-4x+3

=x²-(3+1)x+3

=x²-3x-x+3

=x.x - 3.x - 1.x + 1.3

=x(x-3) -1(x-3)

=(x-3) (x-1)

x-3=0. or. x-1=0

x= 3. x=1

zeroes of polynomial. coefficients

alpha=3. a=1

beta=1. b=-4

c=3

1. sum of zeroes (alpha + beta)=3+1=4
2. product of zeroes (alpha. beta)=3.1=3
3. -b/a =-(-4)/1=4/1=4
4. c/a =3/1=3

therefore, alpha+beta=-b/a

alpha. beta=c/a

Answer 2

SOLUTION

Question ( as corrected by the user in live chat )

: Find the zeroes of the polynomial and verify the Division Algorithm.

Steps:

1) Find the zeroes of the polynomial through any method, Here I chose splitting the middle term.

2) Verify the answer by Division Algorithm, which is

Dividend = Divisor × Quotient + Remainder

3) After finding the zeroes, Say g(x) and g'(x) respectively. On dividing the polynomial with one of these We must get the other one.

4) Substitute the values of Divisor, Quotient and Remainder in the formula, We must get p(x) on doing so.

Verification of Division Algorithm

Dividend = p(x) = x² - 4x + 3

Divisor = g(x) = x - 3

Quotient = g'(x) = x - 1

Remainder = 0

Substitute Values.

Dividend = Divisor × Quotient + Remainder

= g(x) × g'(x) + 0

= (x - 3) × (x - 1)

= x² - x - 3x - 3 × -1

= x² - 4x + 3

= p(x)

Hence, Proved.