Keyword | CPC | PCC | Volume | Score | Length of keyword |
---|---|---|---|---|---|

real rational and unequal | 0.94 | 0.2 | 3524 | 55 | 25 |

real | 0.94 | 0.5 | 6223 | 61 | 4 |

rational | 1.02 | 0.9 | 829 | 20 | 8 |

and | 0.01 | 0.5 | 6028 | 41 | 3 |

unequal | 1.86 | 0.4 | 3724 | 37 | 7 |

Keyword | CPC | PCC | Volume | Score |
---|---|---|---|---|

real rational and unequal | 1.37 | 0.4 | 7148 | 25 |

real rational and unequal roots | 0.96 | 0.7 | 8586 | 49 |

real rational and equal | 1.35 | 1 | 9643 | 50 |

real rational and equal roots | 0.86 | 0.9 | 4117 | 10 |

real rational and equal example | 0.88 | 0.8 | 7997 | 33 |

real rational unequal roots | 1.95 | 0.2 | 6844 | 21 |

So the roots are real and unequal. We cannot say if the roots are rational or irrational since this depends on the exact value of \(k\).

Unequal means that the discrimanent can't equal zero b/c + or -0 will get you roots that are equal. Irrational means that it is a fraction. This means the discriminant cannot be a perfect square.

When a, b, and c are real numbers, a ≠ 0 and the discriminant is positive but not a perfect square then the roots of the quadratic equation ax 2 + bx + c = 0 are real, irrational and unequal. Here the roots α and β form a pair of irrational conjugates. Case VI: b 2 – 4ac > 0 is perfect square and a or b is irrational

If the discriminant is positive and is a perfect square (ex. 36,121,100,625 ), the roots are rational. If the discriminant is positive and is not a perfect square (ex. 84,52,700 ), the roots are irrational. A positive discriminant has two real roots (these real roots can be irrational or rational).