just 2 questions Please answer it :) 1)the decimal expansion of 6/1250 will be terminating after how many places - Maths - Real Numbers

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

Ajanta Trivedi · Accepted Answer

the denominator is 1250 = $2 * 5^{4}$

thus the highest power of the prime factors is 4. therefore it will terminate after 4 decimals.

2.

the given equation is

$p x (x - 3) + 9 = 0 p x^{2} - 3 p x + 9 = 0$

if the equation has equal roots, discriminant = 0

therefore

$(- 3 p)^{2} - 4 * p * 9 = 0 9 p^{2} - 36 p = 0 9 p (p - 4) = 0$

p can not be zero, for p = 0 , the equations becomes linear equation.

thus p = 4.

hope this helps you.

cheers!!

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

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