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Use remainder theorem to prove that x-3 is a factor of x⁴-6x³ + ax + b if 3a+b = 81 |
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Answer» -step explanation:Factors of X 2 −3x+2 are (x−1) and (x−2).Let f(x)=x 4 −px 2 +qSince, f(x) is divisible by (x−1) and (x−2)∴f(1)=0 and f(2)=0⇒f(1)=1 4 −p(1) 2 +q=0and f(2)=2 4 −p(2) 2 +q=01−p+q=0....(i)and 16−4p+q=0....(ii)(i)−(ii), we GET−15+3p=0⇒p=5putting VALUE of p in eq. (i), we get q=4Thus, we getp=5 and q=4. |
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