Question

if both (x-2) and (x-1/2) are factors of px^2+5x+r, then show that p=r

Answer 1

Answer:

Step-by-step explanation:

Given, f(x) = px^2+5x+r  and factors are x-2, x-1/2

Substitute x = 2 in place of equation, we get

= p*2^2+5*2+r=0  

=  4p + 10 + r = 0   ------------  (i)

Substitute x = 1/2 in place of equation.  

 p/4 + 5/2 + r = 0

 p + 10 + 4r = 0  -------------------  (ii)

On solving (i),(ii) we get

4p+r=-10 and p+4r+10=0

4p+r=p+4r

3p=3r   

p = r.

Answer 2

Step-by-step explanation:

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

f(2) = 0

p(2)^2 + 5(2) + r = 0

4p + 10 + r = 0

4p + r = -10 -------------> (1)

f(1/2) = 0

p(1/2)^2 + 5(1/2) + r = 0

p/4 + 5/2 + r = 0

p + 10 + 4r = 0

p + 4r = -10 ----------------> (2)

from (1) and (2)

4p + r = p + 4r

4p - p = 4r - r

3p = 3r

p = r