Date :
if the zeros of polynomial ax^2+bx+c
are
alpha and ß then find the zeros
of polynomial cx^2 – 2bx+ 4a i

1 thought on “Date :<br />if the zeros of polynomial ax^2+bx+c<br />are<br />alpha and ß then find the zeros<br />of polynomial cx^2 – 2bx+ 4a i”

1. Step-by-step explanation:

   Let,

   z be the general zero of ax²+bx+c i.e.

   [tex]z = \alpha \: or \beta [/tex]

   Then,

   az²+bz+c=0

   Let,

   [tex]z = – \frac{2}{y} [/tex]

   Then,

   [tex]a( – \frac{2}{y})^{2} + b( – \frac{2}{y}) + c = 0 [/tex]

   Multiplying both side by y²

   [tex]4a – 2by + cy^{2} = 0[/tex]

   [tex] = cy^{2} – 2by + 4a = 0[/tex]

   But this is the equation whose roots we are looking for.

   We observe that y is the general solution of this equation.

   But y= -2/z

   But

   [tex]z = \alpha \: or \beta [/tex]

   Therefore

   [tex]y = – \frac{2}{ \alpha } \: or \: – \frac{2}{ \ \beta }[/tex]

   This is the required solution.

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