The coefficient of x8 in the polynomial x-1x-2x-3 -x-10 isA- 1025B- 1240C- 1320D- 1440

The correct option is C 1320The coefficient of x^8 is 1.2 + 1.3 + . . . .+ 2.3 + 2.4 + ….. = 1/2 [(1 + 2 + ...10)^2 (1^2 + 2^2 + .... + 10^2)] = 1/2 [ ( 10 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Sum of Coefficients of All Terms

The coefficie...

Question

The coefficient of $x^{8}$ in the polynomial (x – 1) (x – 2) (x – 3) ……. (x – 10) is

1025

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1240

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1320

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

1440

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C 1320
The coefficient of $x^{8}$ is 1.2 + 1.3 + . . . .+ 2.3 + 2.4 + …..
$= \frac{1}{2} [(1 + 2 + . . .10)^{2} - (1^{2} + 2^{2} + . . . . + 10^{2})] = \frac{1}{2} [{(\frac{10 \times 11}{2})}^{2} - \frac{10 \times 11 \times 21}{6}] = \frac{1}{2} [55^{2} - 55 \times 7] = 55 \times 24 = 1320$

Suggest Corrections

Similar questions

Q. The coefficient of

x^{8}

in the polynomial

(x - 1) (x - 2) (x - 3) . . . (x - 10)

Q. In the polynomial

(x - 1) (x - 2) (x - 3) . . . (x - 100),

the coefficient of

x^{99}

is .

Q. The coefficient of

x^{99}

in the polynomial

(x - 1) (x - 2) (x - 3) . . . (x - 100)

Q. In the polynomial (x – 1)(x – 2)(x – 3) . . . . . .(x – 100), the coefficient of

x^{99}

In the polynomial (x - 1)(x - 2)(x - 3)............... .........(x - 100), the coefficient of $x^{99}$ is

Join BYJU'S Learning Program

The coefficient of x8 in the polynomial (x – 1) (x – 2) (x – 3) ……. (x – 10) is

The correct option is C 1320The coefficient of x8 is 1.2 + 1.3 + . . . .+ 2.3 + 2.4 + ….. =12[(1+2+...10)2−(12+22+....+102)]=12[(10×112)2−10×11×216]=12[552−55×7]=55×24=1320

The coefficient of $x^{8}$ in the polynomial (x – 1) (x – 2) (x – 3) ……. (x – 10) is