Question

If (x - 1) exactly divides 5x² – 3x + 2k, the value of k is​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

⚜ QUESTION ⚜

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If (x - 1) exactly divides 5x² – 3x + 2k, find the value of k.

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⚜ ANSWER ⚜

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If x-1 = 0

Then, x = 1

Let f(x) be the polynomial 5x² – 3x + 2k.

∴ f(x) = 5x² – 3x + 2k

=> f(1) = 5×(1)² – 3×1 + 2k

=> f(1) = 5×1×1 – 3×1 +2k

=> f(1) = 5 – 3 + 2k

=> f(1) = 2 + 2k ----------(i)

∵ (x-1) exactly divides polynomial f(x), so it is a zero of polynomial f(x).

BTP,

f(x) = 0

=> 2 + 2k = 0 [ From equation (i) ]

=> 2k = 0 - 2

=> 2k = -2

=> k = $\frac{ - 2}{2}$

=> k = -1

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HENCE, the value of k is -1.

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