Question

22. Find the zeroes of the given quadratic polynomial and verify the
relationship between the zeores and the coefficient: 4t2 - 4t + 1.​

Answer 1

Answer:

4t2 − 4t + 1

To find the zeros of the quadratic polynomial we consider

4t2 − 4t + 1 = 0

4t2 − 2t – 2t + 1 = 0

2t(2t – 1) -1(2t – 1) = 0

(2t – 1)(2t – 1) = 0

2t – 1 = 0 and 2t – 1 = 0

2t = 1 and 2t = 1

s = 1/2 and s = 1/2

∴ The zeroes of the polynomial = 1/2 and 1/2

Sum of the zeroes = -(coefficient of s)/(coefficient of s2)

Sum of the zeroes = -(-4)/4 = 1

Let’s find the sum of the roots = 1/2 + 1/2 = 1

Product of the zeros = Constant term / Coefficient of s2

Product of the zeros =1 / 4

Let’s find the products of the roots = 1/2 × 1/2 = 1/4

Step-by-step explanation:

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