If x-3and x-1/3are both factors of px^2+5x +r ,then ahow that p=r

1.	If x-3and x-1/3are both factors of px^2+5x +r ,then ahow that p=r
Answer» ong>Answer: 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. Step-by-step explanation:

Answer»

ong>Answer:

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.

Step-by-step explanation:

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