Question

answer this step by step please​

Answer 1

$\huge\mathcal{\fcolorbox{cyan}{black}{\pink{ANSWER}}}$

Formula :

$if \: \: \alpha \: \: \: and \: \: \: \beta \: \: are \: the \: zeroes \: of \: \: polinomial \: \\ then \: it \: is \: \\ \\ {x}^{2} - (sum \: of \: zeroes)x + product \: of \: zeroes \\ = {x}^{2} - ( \alpha + \beta )x + \alpha \beta$

1)

Given,

$\alpha + \beta = 4 \\ \alpha \beta = 1 \\ {x}^{2} - 4x + 1$

2)

$\alpha + \beta = 0 \\ \alpha \beta = \sqrt{5} \\ \\ {x}^{2} - 0 \times x + \sqrt{5} \\ = {x}^{2} + \sqrt{5}$

Answer 2

Answer:

General form of the quadratic equation when the roots are given is

2

X -(sum of the roots) x + product of the roots =0

2

1) X -4x + 1 = 0

2) X -0x +√5 =0