Find the zeros of quadratic polynomials and verify the relationship be

1.	Find the zeros of quadratic polynomials and verify the relationship between the zeros and their coefficients:h(s) = 2s2 – (1 + 2√2)s + √2
Answer» Given, 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.

Find the zeros of quadratic polynomials and verify the relationship between the zeros and their coefficients:h(s) = 2s2 – (1 + 2√2)s + √2

Answer»

Given,

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.