Question

find the zeros of the quadratic polynomial 3x square + 4 x + 1 and verify the relationship between the zeros and the coefficients​

Answer 1

root 2/3 , -2/3

I hope this help you.

Answer 2

3x^2+4x+1

p(x)=3x^2+3x+x+1

=3x(x+1)+1(x+1)

=(3x+1)(x+1)

therefore x=-1/3 and x=-1 are the zeros of p(x).

Let α=-1/3 and β=-1,

therefore α+β=-1/3+(-1) & αβ=(-1/3)(-1)

therefore α+β=-4/3. & αβ=1/3...(i)

a=3,b=4 and c=1......(coefficient of p(x))

α+β=-(-4/3) & αβ=1/3......(from i)

α+β=-b/a. & αβ=c/a

HENCE PROVED