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If the equation $x^{2} - kx + 1 = 0$ has no real roots then

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k > 2

none of these

k < - 2

- 2 < k < 2

answer is C.

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Detailed Solution

Given quadratic equation is,

x^{2} - kx + 1 = 0

.
A quadratic equation in the variable x is of the form

a x^{2} + bx + c = 0, a \neq 0

where a, b and c are real numbers and has no real roots if

b^{2} - 4 ac < 0

.
After comparing the given equation

x^{2} - kx + 1 = 0

with the standard form of the quadratic equation, we get,

a = 1, b = - k, c = 1

.
Then,

⟹ b^{2} - 4 ac < 0

⟹ {(- k)}^{2} - 4 \times 1 \times 1 < 0

⟹ k^{2} - 4 < 0

⟹ k^{2} < 4

⟹ - 2 < k < 2

∴

If the equation

x^{2} - kx + 1 = 0

has no real roots then

- 2 < k < 2

Hence, the correct option is 3.

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