# Complex Numbers and Quadratic Equations-Nature of Roots (KVPY Stream-SB-SX Math): Questions 1 - 3 of 3

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## Question number: 1

» Complex Numbers and Quadratic Equations » Nature of Roots

Appeared in Year: 2010

### Question

The roots of are –

### Choices

Choice (4) | Response | |
---|---|---|

a. | Non-real except one positive real root | |

b. | Non-real except for three real roots of which exactly one is positive | |

c. | Non-real except three positive real roots | |

d. | All necessarily real |

## Question number: 2

» Complex Numbers and Quadratic Equations » Nature of Roots

Appeared in Year: 2011

### Question

Consider the cubic equation , where a, b, c are real numbers. Which of the following statements is correct?

### Choices

Choice (4) | Response | |
---|---|---|

a. | If then the equation has all real and distinct roots | |

b. | If then the equation has real and distinct roots | |

c. | If then the equation has one real and two imaginary roots | |

d. | If then the equation has all real roots |

## Question number: 3

» Complex Numbers and Quadratic Equations » Nature of Roots

Appeared in Year: 2012

### Question

Suppose a, b, c are real numbers, and each of the equations and has two distinct real roots. Then the equation has –

### Choices

Choice (4) | Response | |
---|---|---|

a. | Two equal roots | |

b. | No real roots | |

c. | One positive and one negative root | |

d. | Two distinct positive real roots |