Question

Find the polynomial.(-1/3,4) is the solution set of

Answer 1

If the solutsion are r1,r2 then the factored form is
y=a(x-r1)(x-r2) where a is a constant

so

r1=-1/3
r2=4

y=a(x-(-1/3))(x-4)
y=a(x+1/3)(x-4)

so it will be
y=a(x+1/3)(x-4)
a is a constant

Answer 2

Answer: The required polynomial is

$3x^2-11x-4=0$

Step-by-step explanation:

Since we have given that

(-1/3,4) is the solution set

We need to find the polynomial.

Since it has only two roots. So, it must be quadratic polynomial.

$(x+\frac{1}{3})(x-4)\\\\=x(x-4)+\frac{1}{3}(x-4)\\\\=x^2-4x+\frac{1}{3}x-\frac{4}{3}\\\\=x^2+\frac{-12x+x}{3}-\frac{4}{3}\\\\=x^2+(\frac{-11x}{3})-\frac{4}{3}\\\\\implies 3x^2-11x-4=0$

Hence, The required polynomial is

$3x^2-11x-4=0$