Question

Write the word equation whose roots are root 5 minus 4 and root 5 + 4

Answer 1

Step-by-step explanation:

you can verify it by by using the formula of quadratic equation

Answer 2

Step-by-step explanation:

$let \\ \alpha = \sqrt{5 } - 4 \\ \beta = \sqrt{5} + 4 \\sum \: of \: roots \\ \alpha + \beta = \sqrt{5} - 4 + \sqrt{5} + 4 \\ \alpha + \beta = 2 \sqrt{5} \\ product \: of \: roots \\ \alpha \beta = ( \sqrt{5} - 4) ( \sqrt{5} + 4) \\ \alpha \beta = ( { \sqrt{5} })^{2} - ( {4})^{2} \\ \alpha \beta = 5 - 16 \\ \alpha \beta = - 11 \\ for \: forming \: quadratic \: equation \: \\ when \: roots \: are \: given \: by \: the \: formula \\ = k( {x}^{2} - ( \alpha + \beta )x + \alpha \beta ) \\ = k( {x}^{2} - 2 \sqrt{5} x + ( - 11)) \\ = k( {x}^{2} - 2 \sqrt{5} x - 11) \\ so...... \\ the \: quadratic \: equation \: is \\ {x}^{2} - 2 \sqrt{5} x - 11$

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