Question

If both x-2 and x- 1/2 are the factors of px² + 5x + r , Show that p=r
Please 9th class solve it !!!!!! Please no spamming

Answer 1

hey...!!
here is ur answer...!☺☺

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Let,
p(x)=px²+5x+r.

Since,
x-2 ad x-1/2 are factors of p(x).

p(2)=0 and p(1/2)=0
p×2²+5×2+r=0  and  p(1/2)²+5×1/2+r=0
4p+10+r=0 and p/4+5/2+r=0
4p+r=-10 and p+4r+10=0
                         4
4p+r=-10 and p+4r+10=0
4p+r=-10 and p+4r=-10
4p+r=p+4r
3p=3r  
⇒ p=r
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thanks....!!

Answer 2

Let p(x)=px²+5x+r.Since x-2 ad x-1/2 are factors of p(x).
p(2)=0 and p(1/2)=0
p×2²+5×2+r=0 and p(1/2)²+5×1/2+r=0

4p+10+r=0 and p/4+5/2+r=0

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

4p+r=-10 and p+4r+10=0
4p+r=-10 and p+4r=-10
4p+r=p+4r
3p=3r ⇒ p=r