If P ( x ) is a polynomial of degree 5 with P (1)= P (2)= P (3)= P (4)= P (5)=1, then the value of ( P (7)-1/ P (6)-1) is equal to

Question

If P ( x ) is a polynomial of degree 5 with P (1)= P (2)= P (3)= P (4)= P (5)=1, then the value of ( P (7)-1/ P (6)-1) is equal to (A) 5 (B) 6 (C) 30 (D) 7

Tardigrade Admin · Accepted Answer

Clearly, P(x)=a(x-1)(x-2)(x-3)(x-4)(x-5)+1 ∴ (P(7)-1/P(6)-1)=(a ⋅ 6 ⋅ 5 ⋅ 4 ⋅ 3 ⋅ 2/a ⋅ 5 ⋅ 4 ⋅ 3 ⋅ 2 ⋅ 1)=6

Q. If $P (x)$ is a polynomial of degree 5 with $P (1) = P (2) = P (3) = P (4) = P (5) = 1$ , then the value of $\frac{P ( 7 ) - 1}{P ( 6 ) - 1}$ is equal to

5

6

30

7

Clearly, $P (x) = a (x - 1) (x - 2) (x - 3) (x - 4) (x - 5) + 1$
$∴ \frac{P ( 7 ) - 1}{P ( 6 ) - 1} = \frac{a \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2}{a \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1} = 6$

Q. If P(x) is a polynomial of degree 5 with P(1)=P(2)=P(3)=P(4)=P(5)=1, then the value of P(6)−1P(7)−1​ is equal to

5

6

30

7

Clearly, P(x)=a(x−1)(x−2)(x−3)(x−4)(x−5)+1 ∴P(6)−1P(7)−1​=a⋅5⋅4⋅3⋅2⋅1a⋅6⋅5⋅4⋅3⋅2​=6

Q. If $P (x)$ is a polynomial of degree 5 with $P (1) = P (2) = P (3) = P (4) = P (5) = 1$ , then the value of $\frac{P ( 7 ) - 1}{P ( 6 ) - 1}$ is equal to

Clearly, $P (x) = a (x - 1) (x - 2) (x - 3) (x - 4) (x - 5) + 1$
$∴ \frac{P ( 7 ) - 1}{P ( 6 ) - 1} = \frac{a \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2}{a \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1} = 6$