Ex 2.2, 2 (v) - Chapter 2 Class 10 Polynomials

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Ex 2.2, 2 Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. (v)- 1/4, 1/4 Let the polynomial be p(x) = ax2 + bx + c, Sum of zeroes = (−𝟏)/𝟒 − 𝑏/𝑎 = (−1)/4 Assuming a = 1 − 𝑏/1 = (−1)/4 b = 𝟏/𝟒 Product of zeroes = 𝟏/𝟒 𝑐/𝑎 = 1/4 Assuming a = 1 𝑐/1 = 1/4 c = 𝟏/𝟒 Now, a = 1, b = 1/4 and c = 1/4 Hence, the required quadratic polynomial = ax2 + bx + c = x2 +𝟏/𝟒x +𝟏/𝟒 Another quadratic polynomial can be = 4(x2 +𝟏/𝟒x +𝟏/𝟒) = 4x2 + x + 1