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| Relation between the roots of a quadratic equation |
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| Let a and b be the roots of the equation (i), |
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| Then x = a and x = b |
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| Since a and b are the roots of the equations (i) and (ii), both the equations are identical. |
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| Dividing equation (i) by 'a', we get |
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| The equations (ii) and (iii) are identical. |
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| Therefore their corresponding terms must be identical. |
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| i.e., coefficient of x2 = 1 |
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Examples:
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| Find the sum and product of the following quadratic equations without actually solving. |
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| i) |
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| Suggested answer: |
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| Here a = 1, b = -8, c = 7 |
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| ii) |
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| Suggested answer: |
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| Here a = 3, b = -11, c =12 |
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| iii) |
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| Suggested answer: |
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| Here A = p, B = q, C = r |
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| iv) |
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| Suggested answer: |
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| Here a = 5, b = -10, c =12 |
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