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11111nata11111 [884]
3 years ago
10

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

Mathematics
1 answer:
gladu [14]3 years ago
8 0
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
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