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in Polynomials by (51.8k points)
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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).

1 Answer

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Best 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

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