If the equation, x2 - ax + 1 = 0 has two distinct and real roots, then: 1. |a| 2 2. |a| 2 3. |a| 2 4. |a| 2

Comparing x2 - ax + 1 = 0 with ax2 + bx + c = 0 we get, a = 1, b = -a and c = 1. We know that, Discriminant (D) = b2 - 4ac = (-a)2 - 4 × 1 × 1 = a2 - 4 Since equations has distinct real roots, ⇒ D 0 ⇒ a2 - 4 0 ⇒ a2 4 ⇒ |a| ⇒ |a| 2. Hence, option 3 is the correct option.

Mathematics

If the equation, x² - ax + 1 = 0 has two distinct and real roots, then:
|a| ≥ 2
|a| ≤ 2
|a| > 2
|a| < 2

Quadratic Equations

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Answer

Comparing x² - ax + 1 = 0 with ax² + bx + c = 0 we get,

a = 1, b = -a and c = 1.

We know that,

Discriminant (D) = b² - 4ac

= (-a)² - 4 × 1 × 1

= a² - 4

Since equations has distinct real roots,

⇒ D > 0

⇒ a² - 4 > 0

⇒ a² > 4

⇒ |a| > $\sqrt{4}$

⇒ |a| > 2.

Hence, option 3 is the correct option.

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Mathematics

If the equation, x² - ax + 1 = 0 has two distinct and real roots, then:
|a| ≥ 2
|a| ≤ 2
|a| > 2
|a| < 2

Quadratic Equations

Answer

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