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
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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.
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.
pshussain3:
Just before subtract (1) from(2) step you should have mentioned that we should take LCM then it will be (p+9r)/9=-15
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