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===נוסחאת השורשים - תרגילים===
פתרו את המשוואות הבאות בעזרת נוסחאת השורשים לפתרון משוואה ריבועית
<center><math>x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}</math></center>
<center>
<math>
x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}
</math>
</center>
וללא שימוש בפירוק טרינום. בכל תרגיל גם חשבו את הדיסקרימיננטה <math>\Delta=\sqrt{b^2-4ac}</math>:
#<math>\ 6x^2+6x+4=4x^2+2x+4</math>
#<math>3x^2+22x+57=x^2-3</math>
{{6}{x}^{2}+{6}{x}+{4}}
#<math>-x^2+6x-4=-2x^2-4</math>
=
#<math>-x^2+22x+56=-3x^2-4</math>
{{4}{x}^{2}+{2}{x}+{4}}
#<math>2x^2+4x-21=-4x+3</math>
#<math>\ 2x^2+14x+15=3</math>
#<math>x^2+5x+7=-x-1</math>
{{3}{x}^{2}+{22}{x}+{57}}
#<math>x^2+6x+9=1</math>
=
#<math>2x^2-15x+34=x+4</math>
{{x}^{2}{-3}}
#<math>x^2-x-5=1</math>
#<math>-2x^2+14x+28=-4x^2-2x-2</math>
#<math>\
#<math>x^2+5x-3=x-3</math>
{-{x}^{2}+{6}{x}{-4}}
#<math>2x^2-7x-26=-3x+4</math>
=
#<math>2x^2-5=3</math>
{{-2}{x}^{2}{-4}}
#<math>2x^2+4x+1=-1</math>
#<math>\ 2x^2-17x+35=x-1</math>
#<math>-3x^2-9x=-4x^2-3x</math>
{-{x}^{2}+{22}{x}+{56}}
#<math>x^2+2x-26=-2</math>
=
#<math>2x^2+8x+9=1</math>
{{-3}{x}^{2}{-4}}
#<math>-2x^2+4x+1=-3x^2-x-3</math>
#<math>\ x^2+7x+8=-4</math>
#<math>x^2-6x-34=-x^2-2x-4</math>
{{2}{x}^{2}+{4}{x}{-21}}
#<math>x^2-6x+5=-3</math>
=
#<math>2x^2-8x+2=-4</math>
{{-4}{x}+{3}}
#<math>-x^2-4x-6=-3x^2+2x+2</math>
#<math>\ x^2+x-26=4</math>
#<math>2x^2-18x+21=-4x+1</math>
{{2}{x}^{2}+{14}{x}+{15}}
#<math>2x^2+7x+15=x^2-x-1</math>
=
#<math>x^2+x-15=4x+3</math>
{{3}}
#<math>2x^2+5x-11=-3x-1</math>
#<math>\ x^2-x-14=-2x-2</math>
#<math>2x^2-8x+8=2</math>
{{x}^{2}+{5}{x}+{7}}
#<math>6x^2+x+1=4x^2-3x+1</math>
=
#<math>-2x^2-4x-27=-3x^2-2x-3</math>
{-{x}-1}
#<math>x^2+8x+19=3</math>
#<math>5x^2-12x+11=4x^2-4x-4</math>
#<math>\
#<math>3x^2-7x+9=2x^2-2x+3</math>
{{x}^{2}+{6}{x}+{9}}
#<math>3x^2+6x+6=x^2+2x+4</math>
=
#<math>2x^2-18x+22=-4x-2</math>
{1}
#<math>6x-21=-2x^2-1</math>
#<math>\ 2x^2-33=-1</math>
#<math>x^2+7x-7=4x-3</math>
{{2}{x}^{2}{-15}{x}+{34}}
#<math>2x^2+9x+12=x^2+3x+4</math>
=
#<math>4x^2-x+4=2x^2+3x+4</math>
{{x}+{4}}
#<math>2x^2-4x+4=4x-4</math>
#<math>\ x^2+8x-45=-x^2+4x+3</math>
#<math>x^2=1</math>
{{x}^{2}-{x}{-5}}
#<math>x^2-6x+27=4x+2</math>
=
#<math>10x+20=-2x^2-4x</math>
{1}
#<math>x^2-7x-13=-4x-3</math>
#<math>\
{{-2}{x}^{2}+{14}{x}+{28}}
=
{{-4}{x}^{2}{-2}{x}{-2}}
</math>
#<math>\
{{x}^{2}+{5}{x}{-3}}
=
{{x}{-3}}
</math>
#<math>\
{{2}{x}^{2}{-7}{x}{-26}}
=
{{-3}{x}+{4}}
</math>
#<math>\
{{2}{x}^{2}{-5}}
=
{{3}}
</math>
#<math>\
{{2}{x}^{2}+{4}{x}+1}
=
{-1}
</math>
#<math>\
{{2}{x}^{2}{-17}{x}+{35}}
=
{{x}-1}
</math>
#<math>\
{{-3}{x}^{2}{-9}{x}}
=
{{-4}{x}^{2}{-3}{x}}
</math>
#<math>\
{{x}^{2}+{2}{x}{-26}}
=
{{-2}}
</math>
#<math>\
{{2}{x}^{2}+{8}{x}+{9}}
=
{1}
</math>
#<math>\
{{-2}{x}^{2}+{4}{x}+1}
=
{{-3}{x}^{2}-{x}{-3}}
</math>
#<math>\
{{x}^{2}+{7}{x}+{8}}
=
{{-4}}
</math>
#<math>\
{{x}^{2}{-6}{x}{-34}}
=
{-{x}^{2}{-2}{x}{-4}}
</math>
#<math>\
{{x}^{2}{-6}{x}+{5}}
=
{{-3}}
</math>
#<math>\
{{2}{x}^{2}{-8}{x}+{2}}
=
{{-4}}
</math>
#<math>\
{-{x}^{2}{-4}{x}{-6}}
=
{{-3}{x}^{2}+{2}{x}+{2}}
</math>
#<math>\
{{x}^{2}+{x}{-26}}
=
{{4}}
</math>
#<math>\
{{2}{x}^{2}{-18}{x}+{21}}
=
{{-4}{x}+1}
</math>
#<math>\
{{2}{x}^{2}+{7}{x}+{15}}
=
{{x}^{2}-{x}-1}
</math>
#<math>\
{{x}^{2}+{x}{-15}}
=
{{4}{x}+{3}}
</math>
#<math>\
{{2}{x}^{2}+{5}{x}{-11}}
=
{{-3}{x}-1}
</math>
#<math>\
{{x}^{2}-{x}{-14}}
=
{{-2}{x}{-2}}
</math>
#<math>\
{{2}{x}^{2}{-8}{x}+{8}}
=
{{2}}
</math>
#<math>\
{{6}{x}^{2}+{x}+1}
=
{{4}{x}^{2}{-3}{x}+1}
</math>
#<math>\
{{-2}{x}^{2}{-4}{x}{-27}}
=
{{-3}{x}^{2}{-2}{x}{-3}}
</math>
#<math>\
{{x}^{2}+{8}{x}+{19}}
=
{{3}}
</math>
#<math>\
{{5}{x}^{2}{-12}{x}+{11}}
=
{{4}{x}^{2}{-4}{x}{-4}}
</math>
#<math>\
{{3}{x}^{2}{-7}{x}+{9}}
=
{{2}{x}^{2}{-2}{x}+{3}}
</math>
#<math>\
{{3}{x}^{2}+{6}{x}+{6}}
=
{{x}^{2}+{2}{x}+{4}}
</math>
#<math>\
{{2}{x}^{2}{-18}{x}+{22}}
=
{{-4}{x}{-2}}
</math>
#<math>\
{{6}{x}{-21}}
=
{{-2}{x}^{2}-1}
</math>
#<math>\
{{2}{x}^{2}{-33}}
=
{-1}
</math>
#<math>\
{{x}^{2}+{7}{x}{-7}}
=
{{4}{x}{-3}}
</math>
#<math>\
{{2}{x}^{2}+{9}{x}+{12}}
=
{{x}^{2}+{3}{x}+{4}}
</math>
#<math>\
{{4}{x}^{2}-{x}+{4}}
=
{{2}{x}^{2}+{3}{x}+{4}}
</math>
#<math>\
{{2}{x}^{2}{-4}{x}+{4}}
=
{{4}{x}{-4}}
</math>
#<math>\
{{x}^{2}+{8}{x}{-45}}
=
{-{x}^{2}+{4}{x}+{3}}
</math>
#<math>\
{{x}^{2}}
=
{1}
</math>
#<math>\
{{x}^{2}{-6}{x}+{27}}
=
{{4}{x}+{2}}
</math>
#<math>\
{{10}{x}+{20}}
=
{{-2}{x}^{2}{-4}{x}}
</math>
#<math>\
{{x}^{2}{-7}{x}{-13}}
=
{{-4}{x}{-3}}
</math>
===תשובות סופיות===
#<math>\ {-2,0\}</math>
#<math>\{-5,-6\}</math>
\left\{{{-2}},{0}\right\}
#<math>\{-6,0\}</math>
#<math>\{-6,-5\}</math>
#<math>\{-6,2\}</math>
#<math>\{-6,-1\}</math>
#<math>\{-2,-4\}</math>
#<math>\{-2,-4\}</math>
#<math>\{5,3\}</math>
#<math>\{-2,3\}</math>
#<math>\{-5,-3\}</math>
#<math>\{-4,0\}</math>
#<math>\{5,-3\}</math>
#<math>\{-2,2\}</math>
#<math>\{-1\}</math>
#<math>\{6,3\}</math>
#<math>\{0,6\}</math>
#<math>\{-6,4\}</math>
#<math>\{-2,-2\}</math>
#<math>\{-4,-1\}</math>
#<math>\{-3,-4\}</math>
#<math>\{-3,5\}</math>
#<math>\{4,2\}</math>
#<math>\{3,1\}</math>
#<math>\{4,-1\}</math>
#<math>\{5,-6\}</math>
#<math>\{5,2\}</math>
#<math>\{-4\}</math>
#<math>\{-3,6\}</math>
#<math>\{1,-5\}</math>
#<math>\{-4,3\}</math>
#<math>\{1,3\}</math>
#<math>\{-2,0\}</math>
#<math>\{6,-4\}</math>
#<math>\{-4\}</math>
#<math>\{3,5\}</math>
#<math>\{2,3\}</math>
#<math>\{-1\}</math>
#<math>\{3,4\}</math>
#<math>\{2,-5\}</math>
#<math>\{-4,4\}</math>
#<math>\{1,-4\}</math>
#<math>\{-2,-4\}</math>
#<math>\{2,0\}</math>
#<math>\{2\}</math>
#<math>\{-6,4\}</math>
#<math>\{1,-1\}</math>
#<math>\{5\}</math>
#<math>\{-5,-2\}</math>
#<math>\{-2,5\}</math>
[[קטגוריה:אלגברה תיכונית]]
</math>
#<math>\
\left\{{{-5}},{{-6}}\right\}
</math>
#<math>\
\left\{{{-6}},{0}\right\}
</math>
#<math>\
\left\{{{-6}},{{-5}}\right\}
</math>
#<math>\
\left\{{{-6}},{{2}}\right\}
</math>
#<math>\
\left\{{{-6}},{-1}\right\}
</math>
#<math>\
\left\{{{-2}},{{-4}}\right\}
</math>
#<math>\
\left\{{{-2}},{{-4}}\right\}
</math>
#<math>\
\left\{{{5}},{{3}}\right\}
</math>
#<math>\
\left\{{{-2}},{{3}}\right\}
</math>
#<math>\
\left\{{{-5}},{{-3}}\right\}
</math>
#<math>\
\left\{{{-4}},{0}\right\}
</math>
#<math>\
\left\{{{5}},{{-3}}\right\}
</math>
#<math>\
\left\{{{-2}},{{2}}\right\}
</math>
#<math>\
\left\{{-1},{-1}\right\}
</math>
#<math>\
\left\{{{6}},{{3}}\right\}
</math>
#<math>\
\left\{{0},{{6}}\right\}
</math>
#<math>\
\left\{{{-6}},{{4}}\right\}
</math>
#<math>\
\left\{{{-2}},{{-2}}\right\}
</math>
#<math>\
\left\{{{-4}},{-1}\right\}
</math>
#<math>\
\left\{{{-3}},{{-4}}\right\}
</math>
#<math>\
\left\{{{-3}},{{5}}\right\}
</math>
#<math>\
\left\{{{4}},{{2}}\right\}
</math>
#<math>\
\left\{{{3}},{1}\right\}
</math>
#<math>\
\left\{{{4}},{-1}\right\}
</math>
#<math>\
\left\{{{5}},{{-6}}\right\}
</math>
#<math>\
\left\{{{5}},{{2}}\right\}
</math>
#<math>\
\left\{{{-4}},{{-4}}\right\}
</math>
#<math>\
\left\{{{-3}},{{6}}\right\}
</math>
#<math>\
\left\{{1},{{-5}}\right\}
</math>
#<math>\
\left\{{{-4}},{{3}}\right\}
</math>
#<math>\
\left\{{1},{{3}}\right\}
</math>
#<math>\
\left\{{{-2}},{0}\right\}
</math>
#<math>\
\left\{{{6}},{{-4}}\right\}
</math>
#<math>\
\left\{{{-4}},{{-4}}\right\}
</math>
#<math>\
\left\{{{3}},{{5}}\right\}
</math>
#<math>\
\left\{{{2}},{{3}}\right\}
</math>
#<math>\
\left\{{-1},{-1}\right\}
</math>
#<math>\
\left\{{{3}},{{4}}\right\}
</math>
#<math>\
\left\{{{2}},{{-5}}\right\}
</math>
#<math>\
\left\{{{-4}},{{4}}\right\}
</math>
#<math>\
\left\{{1},{{-4}}\right\}
</math>
#<math>\
\left\{{{-2}},{{-4}}\right\}
</math>
#<math>\
\left\{{{2}},{0}\right\}
</math>
#<math>\
\left\{{{2}},{{2}}\right\}
</math>
#<math>\
\left\{{{-6}},{{4}}\right\}
</math>
#<math>\
\left\{{1},{-1}\right\}
</math>
#<math>\
\left\{{{5}},{{5}}\right\}
</math>
#<math>\
\left\{{{-5}},{{-2}}\right\}
</math>
#<math>\
\left\{{{-2}},{{5}}\right\}
</math>
[[קטגוריה: אלגברה תיכונית]]
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