Question

CLASS 9 MATHEMATICS ( POLYNOMIALS )
Q) If x – 3 and x − 1/3 are both factors of px^2 + 5x + r , then show that P = r. PLEASE REPLY SOON. I NEED IT URGENTLY

Answer 1

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+5x+r

>>> P (3)^2 + 5(3) +r = 0

>>> 3p+ r + 15= 0

>>> 9p+r= -15 ……..(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+ 5(1/3) + r=0

>>> P(1/9)+ 5/3 +r =0

>>> P(1/9) + r= -5/3

>>> P + 9r = -15 …(2) simultaneous eqn

Subtract (1) from (2)

>>> 8p - 8r = 0

>>> 8p = 8r

>>> p = r

As required.