Question

4S²- 4S+1
find the zeroes of the quadratic polynomial and verify the relationship between zeroes and the co efficient ​

Answer 1

Answer:

$\alpha = \frac{1}{2} \: \: \: \: and \: \: \: \: \beta = \frac{1}{2}$

Step-by-step explanation:

$4 {s}^{2} - 4s + 1 \\ = 4 {s}^{2} - 2s - 2s + 1 \\ = 2s(2s - 1) \: - 1(2s - 1) \\ = (2s - 1)(2s - 1) \\ s = \frac{1}{2}$

Let the two zeroes be

$\alpha \: \: and \: \: \beta$

So,

$\alpha = \frac{1}{2} \: \: and \: \: \beta = \frac{1}{2}$

And,

$\alpha + \beta = - \frac{b}{a} = - \frac{( - 4)}{4} = 1$

Also,

$\alpha + \beta = \frac{1}{2} + \frac{1}{2} = 1$

And,

$\alpha. \beta = \frac{c}{a} = \frac{1}{4}$

Also,

$\alpha . \beta = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$

Hence, Verified.

Answer 2

Answer:

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