If (x-3) and [x-1/3] are both factors of ax^2+5x+b, then show that a=b - Maths - Polynomials

Question

If (x-3) and [x-1/3] are both factors of ax^2+5x+b, then show
that a=b

Aakash Sharma · Accepted Answer

Given: $(x - 3) and (x - \frac{1}{3})$ are the factors of $a x^{2} + 5 x + b$ $\Rightarrow Product of roots = 3 \times \frac{1}{3} \Rightarrow \frac{b}{a} = 1 \Rightarrow a = b$

If (x-3) and [x-1/3] are both factors of ax^2+5x+b, then show that a=b.