Question

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Answer 1

I hope it will help you

Answer 2

Answer:

Option(A)

Step-by-step explanation:

Note: If the discriminant is greater than 0,then the equation has real roots.

Option Verification:

(a)

x² - 2√3x - 1 = 0.

On comparing with ax² + bx + c = 0, we get

a = 1, b = -2√3, c = -1.

Discriminant (D) = b² - 4ac

                          = (-2√3)² - 4(1)(-1)

                          = 12 + 4

                          = 16 > 0.

(ii)

Given Equation is x^2 + 2x + 4 = 0.

Here, a = 1, b = 2, c = 4.

∴ D = b² - 4ac

     = (2)² - 4(1)(4)

     = 4 - 16

     = -12 < 0.

(iii)

Given Equation is x² - x + 1 = 0

Here, a = 1, b = -1, c = 1

∴ D = b² - 4ac

      = (-1)² - 4(1)(1)

      = 1 - 4

      = -3 < 0

(iv)

Given Equation is 3x² - 2x + 1.

Here, a = 3, b = -2, c = 1

∴ D = b² - 4ac

      = (-2)² - 4(3)(1)

      = 4 - 12

      = -8 < 0.

Therefore, x² + 2√3x - 1 = 0 has real roots.

Hope it helps!