Question

find the zeros of the quadrati. polynomial 6x^2-7x-3 also verify the relation between the sum of zeroes and product of zeroes

Answer 1

6x²-7x-3
by middle term splitting method
6x²-9x+2x-3
3x(2x-3)+1(2x-3)
(2x-3)(3x+1)
when,
2x-3=0
x=3/2
againwhen,
3x+1=0
x=-1/3
zeroes are 3/2 and -1/3
α+β=-b/a
LHS=α+β
=3/2+(-1/3)
=3/2-1/3
=7/6
RHS=-b/a
=-(-7)/6
=7/6
LHS=RHS

α*β=c/a
LHS=α*β
=3/2*-1*3
=-3/6
=-1/2
RHS=c/a
=-3/6
=-1/2
LHS=RHS
hence proved