Find a quadratic equation with the following roots :
a. -3 and 7
[tex] \sf{b. \: - 1 + \sqrt{3} \: \:and \: - 1 \sqrt{3} }[/tex]
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Find a quadratic equation with the following roots :
a. -3 and 7
[tex] \sf{b. \: - 1 + \sqrt{3} \: \:and \: - 1 \sqrt{3} }[/tex]
Help.
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✒ SOLUTION :
[tex] \sf \large \bold{A. \: Let \: r_{1} \: = - 3 \:, r_{2} = 7,and \: Thus,r_{1} \: + \: r_{2} \: = \: - 3 + 7 = 4 } \\ \sf \large \bold{and \: r_{1}r_{2} = - 3 \: . \: 7 = - 21. \: Therefore \: x {}^{2} - 4x + ( - 21) = 0}[/tex]
[tex] \sf \large \bold{x = - 3 \: \: and \: \: x = 7}[/tex]
[tex] \sf \large \bold{Thus, x - ( - 3) = 0 \: \: and \: \: x - 7 = 0}[/tex]
( x + 3 )( x - 7 = 0 )
x² - 4x - 21 = 0
The required quadratic equation is x² - 4x - 21 = 0
[tex] \sf \small \bold{B. \: SUM \: = - 1 + \sqrt{3} + ( - 1 - \sqrt{3} ) = - 2}[/tex]
[tex] \sf \small \bold{PRODUCT \: = ( - 1 + \sqrt{3} ( - 1 - \sqrt{3} ) = 1 - 3 = - 2.}[/tex]
[tex]\sf \blue{\overline{ \:\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }}[/tex]
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