If both (x-3) and (x-1/3) are the factors of (px)square +5x +r , then

1.	If both (x-3) and (x-1/3) are the factors of (px)square +5x +r , then show that p - r = 0plz tell me the write answer urgent hai yarr
Answer» Answer: This question requires that you find the values of p and R, which i assume before solving, are equal. Now, if x-3 and x-1/3 are both factors to this expression , it means their division gives a value of zero. Now LETS use x-3 >>> let x-3=0. >>> x=3 Now substitute x=3 into the expression >>>> Px^2+3x+r >>> P (3)^2 + 3(3) +r = 0 >>> 9p+ r + 9= 0 >>> 9p+r= -9 ……..(1) SIMULTANEOUS eqn Now use x-1/3. Let x-1/3=0 >>> x=1/3 Now substitute x=1/3 into the polynomial >>> P(1/3)^2+ 3(1/3) + r=0 >>> P(1/9)+ 1 +r =0 >>> P(1/9) + r= -1 >>> P + 9r = -9…(2) simultaneous eqn Subtract (1) from (2) >>> 9p+ r =-9 - P + 9r =-9 >>> 8p - 8r = 0 >>> 8p = 8r >>> p = r As REQUIRED.

If both (x-3) and (x-1/3) are the factors of (px)square +5x +r , then show that p - r = 0plz tell me the write answer urgent hai yarr

Answer»

Answer:

This question requires that you find the values of p and R, which i assume before solving, are equal.

Now, if x-3 and x-1/3 are both factors to this expression , it means their division gives a value of zero.

Now LETS use x-3

>>> let x-3=0.

>>> x=3

Now substitute x=3 into the expression

>>>> Px^2+3x+r

>>> P (3)^2 + 3(3) +r = 0

>>> 9p+ r + 9= 0

>>> 9p+r= -9 ……..(1) SIMULTANEOUS eqn

Now use x-1/3.

Let x-1/3=0

>>> x=1/3

Now substitute x=1/3 into the polynomial

>>> P(1/3)^2+ 3(1/3) + r=0

>>> P(1/9)+ 1 +r =0

>>> P(1/9) + r= -1

>>> P + 9r = -9…(2) simultaneous eqn

Subtract (1) from (2)

>>> 9p+ r =-9

P + 9r =-9

>>> 8p - 8r = 0

>>> 8p = 8r

>>> p = r