Find the greatest value of k ∈ N for which the equation x² - 4x + k = 0 has distinct real roots.
-4
3
1
4

Question

Find the greatest value of k ∈ N for which the equation x2 - 4x + k = 0 has distinct real roots. 1. -4 2. 3 3. 1 4. 4

KnowledgeBoat · Accepted Answer

Given, x2 - 4x + k = 0 Comparing x2 - 4x + k = 0 with ax2 + bx + c = 0 we get, a = 1, b = -4 and c = k. Since roots are distinct and real, D 0 ⇒ b2 - 4ac 0 ⇒ (-4)2 - 4(1)(k) 0 ⇒ 16 - 4k 0 ⇒ 16 4k ⇒ k ⇒ k 4 Since k ∈ N, Possible natural numbers less than 4 are: 1, 2, 3 The greatest value is: 3 Hence, Option 2 is the correct option.

Mathematics

Find the greatest value of k ∈ N for which the equation x² - 4x + k = 0 has distinct real roots.
-4
3
1
4

Quadratic Equations

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Find the greatest value of k ∈ N for which the equation x2 - 4x + k = 0 has distinct real roots.-4314

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Find the greatest value of k ∈ N for which the equation x² - 4x + k = 0 has distinct real roots.
-4
3
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4

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If (k + 2)x² - 2x + 1 = 0 has real roots then greater value of k(∈ Z) is :
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