Question

2.Which of the following equations has no real roots



x² - 4x + 3√2 = 0

x² + 4x - 3√2 = 0

x² - 4x - 3√2 = 0

3x² + 4√3x + 4 = 0

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Answer 1

Lets check them one by one,

★ x^2 - 4x + 3√2 = 0

Here, D = b^2 - 4ac

= (-4)-2 - 4(1)(3√2)

= 16 - 12√2

= 16 - 12(1.414)

= 16 - 16.97

= -0.97

Thus, D < 0

=> The equation has no real roots

★ x^2 + 4x - 3√2 = 0

Here, D = b^2 - 4ac

= (4)^2 - 4(1)(-3√2)

= 16 + 12√2

= 16 + 16.97

= 32.97

Thus, D > 0

=> The equation has real roots.

★ x^2 - 4x - 3√2 = 0

Here, D = b^2 - 4ac

= (-4)^2 - 4(1)(-3√2)

= 16 + 12√2

= 16 + 16.97

= 32.97

Thus, D > 0.

=> The equation has real roots.

★ 3x^2 + 4√3x + 4 = 0

Here, D = b^2 - 4ac

= (4√3)^2 - 4(3)(4)

= 48 - 48

= 0

Thus, D = 0

=> The equation has real and equal roots.