Find the series of the quadratic polynomial 6x² - 5x + 1 and verify the relationship between the zeroes and the coefficients
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6x² - 5x + 1
=>6x^2-3x-2x+1=0
=>3x(2x-1)-1(2x-1)=0
=>(3x-1)(2x-1)=o
=>3x-1=0 | 2x-1=0
=> 3x=1 | 2x=1=0
=> x=1/3 | x=1/2
alpha=1/3 , beta=1/2
Sum of the zeros (alpha+ beta)=1/3+1/2
= 5/6
Product of zeros (alpha× beta)=1/3×1/2
=1/6
Relation between the zeros and coefficients:
Sum of the zeros:
=[coefficients of x/coefficient of x^2]
=(-b/a)
=[-(-5/6)]
=(5/6)
Product of zeros:
=[constant/coefficient of x^2]
= (c/a)
= (1/6)
Therefore ,
Sum of the zeros=[5/6]
Product of the zeros=[1/6]
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