Question

. if x-3 and x-1/3 are both factors of px 2 + 5x+r, then show that P = r.

Answer 1

put x= 3 and 1/3. You will get 2 equations. On solving them you will get your answer

Answer 2

Step-by-step explanation:

Given  :

We are given the factors of the quadratic equation

                      $px^2+5x+r=0$

that are  $(x-3)$ and $(x-\frac{1}{3})$

To Prove :  P = r

Solution :

Since we are given the factors of the quadratic equation

$(x-3)$ and $(x-\frac{1}{3})$

Since we can get the quadratic equation by multiplying both the factors

$(x-3)(x-\frac{1}{3})=0$

$x(x-3)-\frac{1}{3}(x-3)=0$

$x^2-3x-\frac{x}{3}+1=0$

multiply both sides by 3

$3(x^2-3x-\frac{x}{3}+1)=0$

$3x^2-9x-x+3=0$

$3x^2-10x+3=0$

divide both sides by -2 of the given equation

$-\frac{3}{2}x^2+5x-\frac{3}{2}=0$

comparing above equation by the given quadratic equation

$px^2+5x+r=0$

we get $p=\frac{-3}{2}$  and $r=\frac{-3}{2}$

Hence we can say that P = r

                                                                                               Hence Proved

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