Question

Please give any one answer of the following Question's​

Answer 1

Answer:

$let \: \alpha = 2 + \sqrt{3} \: and \: \beta = 2 - \sqrt{3} \\ so \: \alpha + \beta = 2 + \sqrt{3} + 2 - \sqrt{3} = 4 \\ \alpha \beta = (2 + \sqrt{3} )(2 - \sqrt{3} ) = 4 - 3 = 1 \\ so \: require \: polynomial \: is \: {x}^{2} - 4x + 1$

after long division

now,

${x}^{2} - 2x - 35 \\ (x - 7)(x + 5) \\ so \: remaining \: zeroes \: are \: 7 \: and \: - 5$

Answer 2

Answer 4:

The two zeroes of the polynomial is 2+√3,2 - √3

Therefore, (x - 2+ 3)(x - 2 - √3) x2 + 4 – 4x - 3

= x² - 4x + 1 is a factor of the given polynomial.

Using division algorithm, we get

x⁴ - 6x³ - 26x² + 138x - 35 = (x² - 4x + 1)(x² – 2x - 35)

So, (x² - 2x – 35) is also a factor of the given polynomial.

x² - 2x - 35 = x² - 7x + 5x - 35

= x(x - 7) + 5(x - 7)

= (x – 7)(x+5)

Hence, 7 and −5are the other zeros of this polynomial.

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