Question

the zeroes of the quadratic polynomal3x -5x-2 and verify the relationship between zetoes and the
coefficients,​

Answer 1

Given polynomial,

3x²-5x-2 = 0

3x²-6x+x-2=0

3x(x-2)+1(x-2)=0

(x-2)(3x+1)=0

x-2=0 ; 3x+1=0

x=2 ; x=-1/3

Therefore, the zeroes of the polynomial are 2 and -1/3

Let α(alpha) =2

β(beta) =-1/3

Sum of zeroes = α+β=2+(-1/3)

=2-1/3

=(6-1)/3

=5/3=-(-5)/3

=-(x coefficient)/x² coefficient

Product of zeroes=αβ=2(-1/3)=-2/3

=constant/x² coefficient

Answer 2

Hey mate here is ur answer

3x²+5x-2=(3x-1) (x+2)(by splitting the middle term method)

Hence the value of 3x²+5x-2 is zero when 3x-1=0 or x+2=0

I.e when x=⅓ or x=-2

So the zeroes of 3x²+5x-2 is zero when x=⅓ and x=-2

Sum of zeroes =⅓+(-2)=-5/3=b/a

Product of zeroes=⅓(-2)=-2/3 =c/a

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