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

Transcript

Ex 2.2, 2 Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. (ii) √2 , 1/3 Let the polynomial be p(x) = ax2 + bx + c, Sum of zeroes = √𝟐 − 𝑏/𝑎 = √2 Assuming a = 1 − 𝑏/1 = √2 b = −√2 Product of zeroes = 𝟏/𝟑 𝑐/𝑎 = 1/3 Assuming a = 1 𝑐/1 = 1/3 c = 𝟏/𝟑 Now a = 1, b = –√2 and c = 1/3 Hence, the required quadratic polynomial = ax2 + bx + c = x2 −√𝟐x + 𝟏/𝟑 Another quadratic polynomial can be = 3(x2 −√2x + 1/3) = 3x2 −𝟑√𝟐x +1