Find the zero of the polynomial x² - 4x + 3​

Zeros are 3 and 1.

GIVEN:

P(x) = x²-4x+3

TO FIND:

Zeros and to verify the relationship between zeros and coefficients.

SOLUTION:

=> x²-4x+3 = 0

=> x²-3x-x+3 = 0

=> (x²-3x)+(-x+3) = 0

=> x(x-3)-1(x-3) = 0

=> (x-3)(x-1) = 0

Either (x-3) = 0

=> x = 3

Either (x-1) = 0

=> x = 1

Formula:

=> Sum of zeroes (α+β) = -(Coefficient of x)/Coefficient of x²

=> Product of zeroes (αβ) = Constant term/ Coefficient of x²

Sum of zeros:

= 3+1

=> -(-4)/1 = -(Coefficient of x)/Coefficient of x²

Product of zeros:

= 3(1)

=> 3/1 = Constant term/ Coefficient of x²

the answer is 3 and 1

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1/4 and 8/3 because:

the reciprocal if 4 is 1/4 because 4 is used as 4/1 and the opposite of that is 1/4. the opposite of 3/8 is 8/3 so that is the answer.