Question

The equation px2 - 50x + 75 = 0 has
two distinct roots.
Also, one of the roots is 9 times the
other.
Find the value of p.
p=​

Answer 1

$x^{2}$Answer:

here is your answer

Step-by-step explanation:j

Px2 -50x + 75=0

Let the roots be and x and y.

Its given that x = 9y

Therefore, x + y = -b/a = - (-(50))/p = 50/p

Also, 9y + y = 50/p

So, p= 50/(10y ) = 5/(y )

And xy = c/a = 75/p

Substituting x = 9y and p= 5/(y ) in above equation

(9y multiplied by y gives 9 y squared)

9y2 (9 y squared) = = 75/(5/(3 ) ) = 75 x (y )/(5 ) = 15y

9y2 ( 9 y squared) = 15y

9 x y x y= 15y ( x here is for multiplication)

One y gets cancelled from both sides

Therefore y = 15/9 = 5/3

Now p = 5/(y ) = 5/( 5/3) = 5 x 3/5

Therefore p = 3

i hope u could understand. usually instead if xy and y we conder alpha and beta

this screeshot will help u understand better i hope

Answer 2

Answer:

18

Step-by-step explanation:

given quadratic equation = px²-50x+75= 0

here , a= p, b= 50 , c= 75

lets take one root as z ,

other root = 9z

sum of the root = - b/a

= - 50/p

-> z+9z = -50/p

-> 10z = -50/p

-> p= -50/10z

p= -10/z

product of roots = c/a

z X 9z = 75/p

9z² = 75/p

p= 25/9z²

-10/z = 25/9z²

so, on solving

z= -5/18

so,

p = 18 ( ans )