Question

if (x-3) and(x-1/3)are both the factiors of ax^2+5x+b then show that a=b​

Answer 1

Answer:

since x-3 is a factor of the given EQ.

therefore X=3 is the solution

ax²+5x+b=0

a(3)²+5(3)+b=0

9a+15+b=0

9a+b=-15......(i)

since x-1/√3 is a factor of the given EQ.

therefore X=1/√3 is the solution

a(1/√3)²+5(1/√3)+b=0

a/3+5/√3+b=0

taking LCM

a+5√3+3√3b=0

a+3√3b=-5√3

multiplying by 9

9a+27√3b=-45√3....(ii)

now you can solve these 2 eq to get value of a and b