Question

Find the zeros of the following quadratic polynomials
and verify the relationship between the zeros and
their co-efficients.
(ii) 2s^2– (1 + 2√2)s + √2​

Answer 1

Answer:

h(s) = 2s2 – (1 + 2√2)s + √2 We put h(s) = 0 ⇒ 2s2 – (1 + 2√2)s + √2 = 0 ⇒ 2s2 – 2√2s – s + √2 = 0 ⇒ 2s(s – √2) -1(s – √2) = 0 ⇒ (2s – 1)(s – √2) = 0 This gives us 2 zeros, for x = √2 and x = 1/2 Hence, the zeros of the quadratic equation are √3 and 1. Now, for verification Sum of zeros = – coefficient of s / coefficient of s2 √2 + 1/2 = – (-(1 + 2√2)) / 2 (2√2 + 1)/2 = (2√2 +1)/2 Product of roots = constant / coefficient of s2 1/2 x √2 = √2 / 2 √2 / 2 = √2 / 2 Therefore, the relationship between zeros and their coefficients is verified.Read more on Sarthaks.com - https://www.sarthaks.com/623570/h-s-2s-2-1-22-s-2