Question 12 - MCQs from NCERT Exemplar - Chapter 2 Class 10 Polynomials

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Question 12 If one of the zeroes of a quadratic polynomial of the form x2 + ax + b is the negative of the other, then it has no linear term and the constant term is negative. (b) has no linear term and the constant term is positive. (c) can have a linear term but the constant term is negative. (d) can have a linear term but the constant term is positive. Let p(x) = x2 + ax + b Since one zero is negative the other ∴ Zeroes of p(x) are 𝜶 and −𝜶 Now, Sum of zeroes = (−𝑩)/𝑨 𝜶 + (−𝜶) = (−𝑎)/1 0 = −a a = 0 ∴ The polynomial becomes p(x) = x2 + b Where b is negative Thus, p(x) has no linear term, .and constant term is negativ e So, the correct answer is (A) Product of Zeroes = 𝑪/𝑨 𝜶 × (−𝜶) = 𝑏/1 −𝜶2 = b b = −𝜶2