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The roots of the equation $2 x^{2} - 6 x + 7 = 0$ are

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real and equal

real, unequal, and rational

real, unequal, and irrational

imaginary

answer is D.

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Detailed Solution

Given quadratic equation is,

2 x^{2} - 6 x + 7 = 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

2 x^{2} - 6 x + 7 = 0

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

a = 2, b = 6, c = 7

.
Then,

b^{2} - 4 ac

= {(6)}^{2} - 4 \times 2 \times 7

= 36 - 56

= - 20 < 0

b^{2} - 4 ac

for the equation

2 x^{2} - 6 x + 7 = 0

is less than zero.

∴

We can conclude that the given equation has no real roots i.e. the roots of the equation are imaginary.
Hence, the correct option is 4.

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