Ex 2.2, 2 (i) - 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. (i) 1/4 , −1 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 𝑐/𝑎 = −1 Assuming a = 1 𝑐/1 = −1 c = −1 Now, a = 1, b = – 1/4 and c = –1 Hence, the required quadratic polynomial = ax2 + bx + c = 1x2 − 1/4x − 1 = x2 − 𝟏/𝟒x − 1 Another quadratic polynomial can be = 4(x2 − 1/4x − 1 ) = 4x2 − x − 4