Question

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

Answer 1

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 2

Step-by-step explanation:

p (x)=px^2+5x+r

x-3=0

x=3

p(3)=p (3)^2+5(3)+r

=p (9)+15+r

1. 9p+15+r

x-1/3=0

x=1×3

x=3

p (3)=p (3)^2+5(3)+r

=p(9)+15+r

2. 9p+15+r

1.=2

9p+15+r=9p+15+r

9p+r=9p+15-15+r

p=r

Thank you. ...........