Question

Write a quadratic ploynomial one zero is 3-root5 and product is 4

Answer 1

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So quadratic equation = $x^{2} -Sx+P$

Here S = Sum and  P = Product


ATQ = $x^{2} +3 \sqrt{5} +4$

Answer 2

The answer is given below :

$if \: (3 - \sqrt{5} ) \: be \: a \: zer o \: of \: the \\ required \: polynimial \: then \\ it \: has \: a \: conjugate \: zero \: (3 + \sqrt{5} ) \\ and \: (3 - \sqrt{5} )(3 + \sqrt{5} ) = 9 - 5 = 4$


Hence the factors of the polynomial are
$(x - (3 + \sqrt{5} )) \: and \: (x - (3 - \sqrt{5} ))$

Therefore, the required polynomial is

$= (x - (3 + \sqrt{5} )) (x - (3 - \sqrt{5} )) \\ \\ = {x}^{2} - (3 - \sqrt{5} + 3 + \sqrt{5} )x + 4 \\ \\ = {x}^{2} - 6x + 4$

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