Question

if both(x-2) and (x-1/2)are the factors of (ax2+5x+b).show that a=b

Answer 1

Let p(x)=ax²+5x+b

Then p(2)=a(2)²+5(2)+b
0=4a+10+b
p(1/2)=a(1/2)²+5(1/2)+b
0=a/4 + 5/2 + b
0=a+10+4b

Therefore,
a+10+4b=4a+10+b
3a=3b
a=b

Answer 2

Answer:

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Step-by-step explanation:

Let p(x)=ax²+5x+b

Then p(2)=a(2)²+5(2)+b

0=4a+10+b

p(1/2)=a(1/2)²+5(1/2)+b

0=a/4 + 5/2 + b

0=a+10+4b

Therefore,

a+10+4b=4a+10+b

3a=3b

a=b

hence proved

by AYUSH

^_~