What is the value of 'a' for the equation x2 + ax + 2a - 3 = 0 has r

1.	What is the value of 'a' for the equation x2 + ax + 2a - 3 = 0 has real roots?1. a ∈ (-\(\rm \infty\), 2]2. a ∈ (2, 6)3. a ∈ (6, \(\rm \infty\))4. (-∞, 2] ∪ [6, ∞)
Answer» Correct Answer - Option 4 : (-∞, 2] ∪ [6, ∞) Concept: The roots of a quadratic equation ax² +bx + c = 0 are real if: b² - 4ac ≥ 0 Calculation: Given equation x2 + ax + 2a - 3 = 0 ⇒ x2 + ax + (2a - 3) = 0 So, for real roots: a² - 4 × 1 × (2a - 3) ≥ 0 ⇒ a² - 8a + 12 ≥ 0 ⇒ (a - 6)(a - 2) ≥ 0 ⇒ a ∈ (-∞, 2] ∪ [6, ∞)

What is the value of 'a' for the equation x2 + ax + 2a - 3 = 0 has real roots?1. a ∈ (-\(\rm \infty\), 2]2. a ∈ (2, 6)3. a ∈ (6, \(\rm \infty\))4. (-∞, 2] ∪ [6, ∞)

Answer» Correct Answer - Option 4 : (-∞, 2] ∪ [6, ∞)

Concept:

The roots of a quadratic equation ax² +bx + c = 0 are real if:

b² - 4ac ≥ 0

Calculation:

Given equation x2 + ax + 2a - 3 = 0

⇒ x2 + ax + (2a - 3) = 0

So, for real roots:

a² - 4 × 1 × (2a - 3) ≥ 0

⇒ a² - 8a + 12 ≥ 0

⇒ (a - 6)(a - 2) ≥ 0

⇒ a ∈ (-∞, 2] ∪ [6, ∞)

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What is the value of 'a' for the equation x2 + ax + 2a - 3 = 0 has real roots?1. a ∈ (-\(\rm \infty\), 2]2. a ∈ (2, 6)3. a ∈ (6, \(\rm \infty\))4. (-∞, 2] ∪ [6, ∞)

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