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How many quadratic equations can be formed using numbers from 0, 2, 4, 5 as coefficient if a coefficient can be repeated in an equation.

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#### Solution

Let the quadratic equation be

ax^{2} + bx + c = 0, a ≠ 0

Coefficient |
Values |
Numbers of ways |

a | 2, 4, 5 | 3 |

b | 0, 2, 4, 5 | 4 |

c | 0, 2, 4, 5 | 4 |

Required number = 3 × 4 × 4 = 48

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