Question

If one of the zeros of 3x^2+5x+γ=0 is 4 times the other, then find the zero and value of k

Answer 1

Explanation:

Let α be one of the zeros of the polynomial.

Other = 4α

α + 4α = - Coefficient of x / Coefficient of x² = -5/3

5α = -5/3

α = -5/3*5

α = -1/3

α * 4α = Constant term/Coefficient of x²

4α² = k / 3

`4*((-1)/(3))^(2)=(k)/(3)\\\\4*(1)/(9)=(k)/(3)\\\\4*(1)/(9)*3=k\\\\4*(1)/(3)=k\\\\k=(4)/(3)`