Question

factorize f(x) = 6x^2-x-2 and verify the relation between the zeros and the coefficients​

Answer 1

6x²-x-2=0

6x²-4x+3x-2=0

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

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

so,

2x+1=0

2x=-1

x=-1/2

or

3x-2=0

3x=2

x=2/3

Now, sum of zeroes= -b/a

-1/2 +2/3 = -(-1)/6

-1×3+2×2 = -1/6

6

(-3+4)/6 = 1/6

1/6 = 1/6

L.H.S = R.HS

Product of zeroes = c/a

-1/2 × 2/3 = -2/6

-2/6 = -2/6

L.H.S = R.H.S