Let P(x)=x6+a x5+b x4+c x3+d x2+e x+f be a polynomial such that P(1)=1 ; P(2)=2; P(3)=3 ; P(4)=4 ; P(5)=5 and P(6)=6. If P(7)=k, then find the value of [(k/73)], where [.] denotes the greatest integer function.

Question

Let P(x)=x6+a x5+b x4+c x3+d x2+e x+f be a polynomial such that P(1)=1 ; P(2)=2; P(3)=3 ; P(4)=4 ; P(5)=5 and P(6)=6. If P(7)=k, then find the value of [(k/73)], where [.] denotes the greatest integer function. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

P(x)=(x-1)(x-2)(x-3) ×(x-4)(x-5)(x-6)+x P (7)=727= k ; [(727/73)]

Q. Let $P (x) = x^{6} + a x^{5} + b x^{4} + c x^{3} + d x^{2} + e x + f$ be a polynomial such that $P (1) = 1; P (2) = 2$ ; $P (3) = 3; P (4) = 4; P (5) = 5$ and $P (6) = 6$ . If $P (7) = k$ , then find the value of $[\frac{k}{73}]$ , where $[$ . $] d e n o t es$ the greatest integer function.

$P (x) = (x - 1) (x - 2) (x - 3) \times (x - 4) (x - 5) (x - 6) + x$
$P (7) = 727 = k;$
$[\frac{727}{73}]$

Q. Let P(x)=x6+ax5+bx4+cx3+dx2+ex+f be a polynomial such that P(1)=1;P(2)=2; P(3)=3;P(4)=4;P(5)=5 and P(6)=6. If P(7)=k, then find the value of [73k​], where [.]denotes the greatest integer function.

P(x)=(x−1)(x−2)(x−3)×(x−4)(x−5)(x−6)+x P(7)=727=k; [73727​]

Q. Let $P (x) = x^{6} + a x^{5} + b x^{4} + c x^{3} + d x^{2} + e x + f$ be a polynomial such that $P (1) = 1; P (2) = 2$ ; $P (3) = 3; P (4) = 4; P (5) = 5$ and $P (6) = 6$ . If $P (7) = k$ , then find the value of $[\frac{k}{73}]$ , where $[$ . $] d e n o t es$ the greatest integer function.

$P (x) = (x - 1) (x - 2) (x - 3) \times (x - 4) (x - 5) (x - 6) + x$
$P (7) = 727 = k;$
$[\frac{727}{73}]$