P(x)=2x³-x²+kx-4.
Divide p(x) by x-2 remainder will be 6. Find k
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Answer:
k = -1
Concept used:
p(x) divided by (x - a) leaves remainder p(a).
Step-by-step explanation:
p(x) = 2x³ - x² + kx - 4 = 0
Here, p(x) divided by (x - 2) leaves remainder 6.
∴ p(2) = 6
⇒ 2(2)³ - (2)² + k(2) - 4 = 6
⇒ 2 × 8 - 4 + 2k - 4 = 6
⇒ 16 - 4 + 2k - 4 = 6
⇒ 2k + 8 = 6
⇒ 2(k + 4) = 2 × 3
⇒ k + 4 = 3
⇒ k = 3 - 4
⇒ k = -1
Thus the value of k is -1.
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