Question

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

Answer 1

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

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