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Most Important Selected Qs for JEE AdvancedMathematicsQuadratic Equation

Let f be monic cubic polynomial such that f(1)=1^4-1, f(2)=2^4-2 and f(3)=3^4-3 . If f(4)=N , then find the number of prime factors of N .

Correct answer

3

Step-by-step solution

f(x)=(x-1)(x-2)(x-3)(c-x)+x^4-x Coefficient of x^3=1 c+1+2+3=1 c=-5 aligned & f(x)=(x-1)(x-2)(x-3)(-5-x)+x^4-x & f(4)=3 2 1(-9)+4^4-4=198=2 3^2 11 aligned

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