Quadratic Equations - Playing with the Discriminant
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The document discusses solving a quadratic equation with integer roots. For the equation x^2 - 11x + |p| = 0 to have integer roots, the discriminant must be a perfect square. The discriminant is calculated to be 121 - 4|p|. For the discriminant to be a perfect square, |p| can take the values 0, 10, 18, 24, 28, 30. Therefore, the number of integer values p can take is greater than 8.
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Quadratic Equations - Playing with the Discriminant
- 2. Quadratic Equations x2 – 11x + |p| = 0 has integer roots. How many integer values can ‘p’ take? (a) 6 (b) 4 (c) 8 (d) greater than 8
- 3. Quadratic Equations x2 – 11x + |p| = 0 has integer roots. How many integer values can ‘p’ take? To start with the discriminant should be a perfect square. Let us assume Discriminant = D. The roots will be : 𝑥1 = 11+ 𝐷 2 and 𝑥2 = 11− 𝐷 2
- 4. Quadratic Equations x2 – 11x + |p| = 0 has integer roots. How many integer values can ‘p’ take? Discriminant should be a perfect square and be square of an odd number. D = 112 – 4|p| = 121 – 4|p| 4|p| cannot be negative => D can take values 121, 81, 49, 25, 9, 1 |p| can be 0, 10, 18, 24, 28, 30 p can take 0, ±10, ± 18, ± 24, ± 28, ± 30 (more than 8 values)
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