Question

X-3 and x-1/3 are factors of ax^2+5x+b,show that a=-3/2

Answer 1

Hello,

$ax^2+5x+b=a(x^2+ \frac{5}{a}*x+ \frac{b}{a})\\ =k(x-3)(x- \frac{1}{3})\\ =k(x^2-3x- \frac{1}{3}*x+1)\\ =k(x^2- \frac{10}{3}*x+1)\\ x^2--\ \textgreater \ k=a\\ x--\ \textgreater \ 5=-a* \frac{10}{3} ==\ \textgreater \ a=- \frac{3}{2} \\ x^0--\ \textgreater \ b=a$