if (x-4) and (x-1/4) are the factors of (ax²-5x+b) show that a=b
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Answer:let p(x)=ax²+5x+b,
since (x-4) is a factor of polynomial,
then
p(4)=0,
a×4²+5×4+b=0,
16a+20+b=0,.......eq(1),
since (x-1/4) is a factor of p(x), then
p(1/4) =0,
a×(1/4)²+5×1/4+b=0,
a/16 + 5/4 +b=0,
a+20 + 16b=0,.........eq(2),
on solving by elimination method we will get
a=b
Step-by-step explanation:
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