Binomial Theorem And Coordinate Geometry

University:
Stanford University
Course:
Introduction to Mathematical Thinking
Academic year:

2023
Views:

382

Pages:

4
Author:

MAlphen

Binomial Theorem 1. The first three terms in the expansion of (𝑥 + 4)(1 − 𝑘𝑥)𝑛 are 4 − 7𝑥 + and 26 𝑥2 + ⋯ , where 𝑘 5 𝑛 are constants. Determine the values of 𝑘 and 𝑛. 1 Ans 𝑘 = , 𝑛 = 10 5 : 2. Given that the coefficient of 𝑥4 in the expansion of (i) Find the value of (𝑥3 − 𝑚 )8 is 7, 𝑥 4 𝑚. (ii) Hence, find the term independent of 𝑥 in the expansion of (1 + 𝑥4 Ans: (i) − 2 )(𝑥38− 𝑥 𝑚 ) . 1 (ii) 63 16 2 3. In the expansion of (2 + 𝑥)𝑛, the ratio of the coefficients of 𝑥 and 𝑥2 is 2: 3. Find the value of 𝑛. Ans: Coordinate Geometry The diagram shows a parallelogram with vertices 𝐴(−1, 4), 𝐵(𝑝, 6), 𝐶(4, −1) and 𝐷. (i) Given that 𝐴𝐶 is perpendicular to 𝐵𝐷, show that 𝑝 = 6. (ii) Find the coordinates of 𝐷. (iii) Find the area of the parallelogram 𝐴𝐵𝐶𝐷. Ans: