7/21/2019 4. Quadratic Equations

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Xjgi f pd`yidaof` b(x) os gquftgl td zgrd, wg hgt fi gquftodi wjoej os nidwi fs f pd`yidaof` gquftodi. Ob b(x) os

`oigfr pd`yidaof tjfi b(x) 1 ; os ef``gl f `oigfr gquftodi. Bdr gxfap`g, 5x 3 1 ;,

7/21/2019 4. Quadratic Equations

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Sddts db quflrftoe gquftodi = x 1 os sfol td cg rddt db tjg quflrftoe gquftodi fx3 + cx + e 1 ;, f ; obb x 1 sftosbogs tjgquflrftoe gquftodi o.g. oi dtjgr wdrls tjg vf`ug db f 3 + c + e os zgrd.

Ud`voih f quflrftoe gquftodi =\jg lgtgraoiftodi db f`` tjg rddts db f quflrftoe gquftodi os ef``gl sd`voih tjgquflrftoe gquftodi.

Gx.6 Ejgen wjgtjgr tjg bd``dwoih frg quflrftoe gquftodis =(o) (x + 6)31 (x 5) (oo) (x 3) (x + 6) 1 (x 6) (x + 5) (ooo) (x 5) (3x + 6) 1 x (x + 7)

Ud`. (o) Jgrg, tjg hovgi gquftodi os (x + 6)

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1 3(x 5) ;26332363 33 1+++1++ xxxxxx ;8.;;8 33 1++1+ xxx , wjoej os db tjg bdra ;3 1++ ecxfx

Jgieg, (x + 6)3

1 3(x 5) os f quflrftoe gquftodi.(oo) Jgrg, tjg hovgi gquftodi os (x 3)(x + 5) 1 (x 6) (x + 5)

;65;5335533 3333 1+1++1+ xxxxxxxxxx ,

wjoej os idt db tjg bdra ;3 1++ ecxfx Jgieg, (x 3) (x + 6) 1 (x 6) os idt f quflrftoe gquftodi.

(ooo) Jgrg, tjg hovgi gquftodi os (x 5) (3x + 6) x (x + 7)

;56;;57737523 33333 11+1+ xxxxxxxxxxx ,wjoej os db tjg bdra ;3 1++ ecxfx Jgieg, (x 5) (3x + 6) 1 x(x + 7) os f quflrftoe gquftodi.

Gx.3 Oi gfej db tjg bd``dwoih, lgtgraoig wjgtjgr tjg hovgi vf`ugs frg tjg sd`utodi db tjg hovgi gquftodi dr idt =

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