Question

the polynomials 2x^3+kx^2+3x-5 and x^3+x^2-2x+2k, when divided by (x-3), leave the same remainder find the value of k

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Answer 1

Step-by-step explanation:

Let p(x) = 2x³ + kx² + 3x - 5

Let q(x) = x³ + x² - 2x + 2k

x-3 = 0

x = 3

Put x=3 in p(x)

p(3) = 2(3)³ + k(3)² + 3(3) - 5

= 2(27) + k(9) + 9 -5

= 54 + 9k - 5

= 49 + 9k

Put x=3 in q(x)

q(3) = (3)³ + (3)² - 2(3) + 2k

= 27 + 9 - 6 + 2k

= 30 + 2k

As both the polynomials leave the same remainder so:

p(x) = q(x)

49 + 9k = 30 + 2k

49 -30 = -9k + 2k

19 = -7k

19/-7. = k

Therefore, k= 19/-7