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Chapter 2 Class 10 Polynomials
Serial order wise

If x − 1 is a factor of the polynomial p(x) = x3 + ax² + 2b and a + b = 4, then

(a) a = 5, b = −1 

(b) a = 9, b = −5 

(c) a = 7, b = −3 

(d) a = 3, b = 1

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Question 4 If x − 1 is a factor of the polynomial p(x) = x3 + ax² + 2b and a + b = 4, then (a) a = 5, b = −1 (b) a = 9, b = −5 (c) a = 7, b = −3 (d) a = 3, b = 1 Since x − 1 is a factor of polynomial p(x) ∴ x = 1 is a zero of p(x) Since x = 1 is a zero, ∴ p(1) = 0 (1)3 + a(1)² + 2b = 0 1 + a + 2b = 0 a + 2b = −1 Now, our equations re a + b = 4 …(1) a + 2b = −1 …(2) Doing (2) − (1) (a + 2b) − (a + b) = −1 − 4 a + 2b − a − b = −5 b = −5 Only option (b) matches So, the correct answer is (b)

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.