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# JEE MAIN

If f(x) = x^4 + ax^3 + bx^2 + cx + d, and f(2)= 1, f(3) = 2, f(4) = 3, f(5) = 4, what is the value of a + b + c + d ? Please find it out as soon as possible. I am having problems in finding it out

Note by Eshan Abbas
2 years, 5 months ago

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Let $$g(x) = f(x) - x + 1$$.Then $$g(x)$$ is of degree $$4$$. And for $$x =2,3,4,5$$, $$g(x) = 0$$.This implies $$2,3,4,5$$ are the roots of $$g(x)$$.

Thus we can write $$g(x) = (x-2)(x-3)(x-4)(x-5)$$

$$\Rightarrow f(x) - x + 1 = (x-2)(x-3)(x-4)(x-5)$$

$$\Rightarrow x^4 + ax^3 + bx^2 + cx + d - x + 1 = (x-2)(x-3)(x-4)(x-5)$$.

Putting $$x = 1$$

$$\Rightarrow 1^4 + a*1^3 + b*1^2 + c*1 + d - 1 + 1 = (1-2)(1-3)(1-4)(1-5)$$

$$\Rightarrow a+b+c+d = 24-1 = 23$$. · 2 years, 5 months ago

I think that g(x) should be equal to f(x) - x + 1 · 2 years, 5 months ago

Thanks. Corrected. Hopefully correct now. · 2 years, 5 months ago