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If the difference of the roots of x2 - px + 5 = 0 is 4, then p = ?
1. ± 2
2. ± 6
3. 2
4. 6

1 Answer

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Best answer
Correct Answer - Option 2 : ± 6

Concept:

If α and β are the roots of the quadratic equation ax2 + bx + c = 0,then α + β = -b/a, αβ = c/a.

Calculation:

Given quadratic equation x2 - px + 5 = 0

Let α and β be the roots of the equation x2 - px + 5 = 0

As we know that if roots of quadratic equation ax2 + bx + c = 0 are α and β,then α + β = - b/a, αβ = c/a

⇒ α + β  = p, αβ = 5.

It is given that |α - β|  = 4.

(α + β)2  = (α - β)2 + 4αβ 

⇒ (p)2 = (4)2 + 4 ⋅ 5 = 16 + 20  

⇒ p2 = 36  ⇒ p = ± 6

Hence, option 2 is correct.

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