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4-2.Quadratic Equations and Inequations
hard
જો સમીકરણનો $ax^3 + bx + c$ નો એક ઘટક $x^2 + px + 1$ હોય, તો.....
A
$a^2 + c^2 = -ab$
B
$a^2 - c^2 = -ab$
C
$a^2 - c^2 = ab$
D
આપેલ પૈકી એકપણ નહિ.
Solution
તે ઘટક છે જો $ax^3 + bx + c =(x^2 + px + 1) (ax + c)$
$ \Rightarrow \,c\,\, + \,\,ap\,\, = \,\,0,\,\,pc\, + \,\,a\,\, = \,\,b$
$\, \Rightarrow \,p\,\, = \,\,\frac{{ – c}}{a}\,\, = \,\,\frac{{b\, – \,a}}{c}\,\,$
$ \Rightarrow \,\,ab\,\, – \,\,{a^2}\, = \,\, – {c^2}\, \Rightarrow \,\,{a^2} – {c^2} = ab$
Standard 11
Mathematics
