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# quadratic methods

Question | Answer |
---|---|

Define Quadratic equation | A second degree equation written as ax^2+bx+c=0 |

solve 2x^2+5x+3=0 | x=(-5±√(5^2-4*2*3))/(2*2) x=(-5±√(25-24))/4 x=(-5±√1)/4 x=(-5±1)/4 x=(-5+1)/4 or (-5-1)/4 x=-1 or x= - 3/2 |

4x^2=8x-13 | 4x^2-8x+13=0 x=(-(-8±√(-8^2-4*4*13))/2*4 x=(8±√(64-208))/(8) x=(8±√-144)/8 x=1+(3/2)i and 1-(3/2)i |

b^2-4ac is called what? | the discriminant |

if b^2-4ac=0 | the equation has 2 real numbers |

if b^2-4ac>0 | the equation has 2 unreal number solutions |

if b^2-4ac<0 | the equation has two complex number soultions |

find discrimant results for x^2-4x-5=0 | b^2-4ac (a=1, b=4, c=-5) (-4)^2-(4*1*5) 16+20=36 36>0 therfore the equation has 2 unequal real number solutions |

find discrimant results for 4x^2-2+5=0 | b^2-4ac (a=4, b=-2, c=5 (2)^2-(4*4*5) 4-80=-76 -76<0 therefore this equation has 2 complex number soultions |

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