Question

please solve this.. and also tell from which book this question has been taken

Answer 1

If (x-2) and (x-1/2) are factors of p(x), then p(2) and p(1/2)= 0
p(x) = px²+5x+r
p(2) = p(2)²+5(2)+r
4p+r+10 = 0
p(1/2)= p(1/2)²+5(1/2)+r
1/4p+r+5/2=0

4p+r+10=1/4p+r+5/2
4p-1/4p+r-r=5/2-10
15/4p=-15/2
p=-15/2×4/15
p=-2

4p+r+10=0
4(-2)+r=-10
r-8=-10
r= -10+8
r=-2

p=r=-2

I don't know from which book it has been taken
Hope it helps ☺
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