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Find the Value of ‘K’ If (X – 2) is a Factor of X3 + 2x2 – Kx + 10. Hence Determine Whether (X + 5) is Also a Factor. - ICSE Class 10 - Mathematics

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Question

Find the value of ‘k’ if (x – 2) is a factor of x3 + 2x2 – kx + 10. Hence determine whether (x + 5) is also a factor.

Solution

p(x) = x^3 + 2x^2 - kx + 10

For (x - 2) to be the factor of p(x) = x3 + 2x2 – kx + 10

p(2) = 0

Thus (2)3 + 2(2)2 – k(2) + 10 = 0

⇒ 8 + 8 – 2k + 10 = 0

⇒ k = 13

Thus p(x) becomes x3 + 2x2 –13x + 10

Now, (x+5) would be the factor of p(x) iff p(–5) = 0

p(–5) = (–5)3 + 2(–5)2 – 13(–5) + 10 = –125 + 50 + 65 + 10 = 0

Thus, (x + 5) is also a factor of p(x).

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APPEARS IN

 2010-2011 (March) (with solutions)
Question 1.1 | 3.00 marks

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Solution Find the Value of ‘K’ If (X – 2) is a Factor of X3 + 2x2 – Kx + 10. Hence Determine Whether (X + 5) is Also a Factor. Concept: Factor Theorem.
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