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Solution.

Given equation is 2x^{2} + 11 = x^{2} + 12

Converting given equation into Standard Form of Quadratic Equation. ax^{2} + bx + c = 0

2x^{2} + 11 = x^{2} + 12 converted into x^{2} + 0x - 1 = 0

Comparing it with the standard Form of Quadratic Equation ax^{2} + bx + c = 0

As we know, discriminant = b^{2} - 4ac

Discriminant = (0)^{2} - 4(1)(-1)

Discriminant = 0 - (-4)

Using quadratic formula

Roots(x_{1}, x_{2}) = | −b ± √ b2 − 4ac |

2a |

Roots(x_{1}, x_{2}) = | −b ± √ D |

2a |

x_{1} = | −b + √D |

2a |

= | −(0) + √4 |

2(1) |

= | 0 + 2 |

2 |

= 1 |

x_{2} = | −b - √D |

2a |

= | −(0) - √4 |

2(1) |

= | 0 - 2 |

2 |

= -1 |

Sum of roots = -b/a

Sum of roots = -(0)/(1)

Product of roots = c/a

Product of roots = (-1)/(1)

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