The number of polynomials having zeroes as –2 and 5 is ______.

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The number of polynomials having zeroes as –2 and 5 is more than 3. Explanation: According to the question, The zeroes of the polynomials = –2 and 5 We know that the polynomial is of the form, p(x) = ax2 + bx + c. Sum of the zeroes = – (Coefficient of x) $\div$ Coefficient of x2 i.e. Sum of the zeroes = – b/a – 2 + 5 = – b/a 3 = – b/a b = – 3 and a = 1 Product of the zeroes = Constant term $\div$ Coefficient of x2 i.e. Product of zeroes = c/a (–2)5 = c/a – 10 = c Substituting the values of a, b and c in the polynomial p(x) = ax2 + bx + c. We get, x2 – 3x – 10 Therefore, we can conclude that x can take any value.

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