In a polynomial p(x) = 2x3 – 7x2 + kx + 20,p(2) = p(3).a. Find the v

1.	In a polynomial p(x) = 2x3 – 7x2 + kx + 20,p(2) = p(3).a. Find the value of k. b. Using the value of k, write the polynomial. c. Find p(1).
Answer» a. p(2) = 2 × 2² – 7 × 2² + k × 2 + 20 = 16 – 28 + 2k + 20 = 8 + 2k p(3) = 2 × 3³ – 7 × 3² + k × 3 + 20 = 54 – 63 + 3k + 20 = 11 + 3k P(2) = P(3) 8 + 2k = 11 + 3k k = -3 b. p(x) = 2x³ – 7x² - 3x + 20 c. p(1) = 2 – 7 – 3 + 20 = 12

In a polynomial p(x) = 2x3 – 7x2 + kx + 20,p(2) = p(3).a. Find the value of k. b. Using the value of k, write the polynomial. c. Find p(1).

Answer»

a. p(2) = 2 × 2² – 7 × 2² + k × 2 + 20

= 16 – 28 + 2k + 20 = 8 + 2k

p(3) = 2 × 3³ – 7 × 3² + k × 3 + 20

= 54 – 63 + 3k + 20 = 11 + 3k

P(2) = P(3)

8 + 2k = 11 + 3k

k = -3

b. p(x) = 2x³ – 7x² - 3x + 20

c. p(1) = 2 – 7 – 3 + 20 = 12