Question

If both (x – 2 ) and (x – ½ ) are factors of px2+ 5x+ r, then show that p – r = 0.

Answer 1

Step-by-step explanation:

here, (x-2) is a factor.

So, x=2 and (x-1/2) is a factor.

hence, x=1/2.

Now, p(x) =px2+5x+r=0

p(2)=p×(2)2+5×2+r=0

0=4p+10+r

-10=4p+r eq. 1

p(1/2)=p×(1/2)2+5×1/2+r=0

0=1/4p+5/2+r

0=(p+10+4r)/4

0×4=p+10+4r

-10=p+4r eq. 2

Solve by subtracting eq. 2 from eq. 1

4p+r=-10

p+4r=-10

- - +

----------------

3p-3r=0

3(p-r) =0×3

(p-r) =0

Hence proved, p-r=0

thanks for your support.