Question

just 2 questions. Please answer it :) 1)the decimal expansion of 6/1250 will be terminating after how many places of decimals? (how to find this ?) 2)find the value of p so that the quadratic equation p x(x-3) + 9 = 0 is has two equal roots

Answer 1

1) 6/1250 = 6/(5^4*2) = ( 6* 2³)/(5^4*2*2³)= 48/(10^4) = 0.0048
2) px(x-3)+9=0
⇒px²-3px+9=0
compare it with ax²+bx+c=0
a=p, b=-3p, c=9

if two root are equal
b²=4ac
(-3p)²=4*p*9
9p²=36p
p²/p =36/9
p=4