If polynomial ax2 +3x2 -3 and 2x3 - 5x + a leaves the same remaninder whan each is divided x-4 ,find the value of a.
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dividing
p(x)=ax^2+3x^2-3 by x-4, we have p(4) as remainder [by reminder theorem]
p(x)=16a+48-3
p(x)=16a+45
now 2nd polynomial
similarly, on divinding 2x^3-5x+a by x-4,as remainder we have;
p(x)=128-20+a
p(x)=108+a
since both the polynomials leave same remainder
16a+45=108+a
16a-a=108-45
15a=63
a=63/15
a=4.2
Hence,a=4.2
p(x)=ax^2+3x^2-3 by x-4, we have p(4) as remainder [by reminder theorem]
p(x)=16a+48-3
p(x)=16a+45
now 2nd polynomial
similarly, on divinding 2x^3-5x+a by x-4,as remainder we have;
p(x)=128-20+a
p(x)=108+a
since both the polynomials leave same remainder
16a+45=108+a
16a-a=108-45
15a=63
a=63/15
a=4.2
Hence,a=4.2
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