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# In the Following, Determine Whether the Given Quadratic Equation Have Real Roots and If So, Find the Roots: 2x^2-2sqrt6x+3=0 - Mathematics

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#### Question

In the following, determine whether the given quadratic equation have real roots and if so, find the roots:

2x^2-2sqrt6x+3=0

#### Solution

We have been given, 2x^2-2sqrt6x+3=0

Now we also know that for an equation ax2 + bx + c = 0, the discriminant is given by the following equation:

D = b2 - 4ac

Now, according to the equation given to us, we have,a = 2, b=-2sqrt6 and c = 3.

Therefore, the discriminant is given as,

D=(-2sqrt6)^2-4(2)(3)

= 24 - 24

= 0

Since, in order for a quadratic equation to have real roots, D ≥ 0.Here we find that the equation satisfies this condition, hence it has real and equal roots.

Now, the roots of an equation is given by the following equation,

x=(-b+-sqrtD)/(2a)

Therefore, the roots of the equation are given as follows,

x=(-(2sqrt6)+-sqrt0)/(2(2))

=(-sqrt6+-0)/2

=-sqrt(3/2)

Therefore, the roots of the equation are real and equal and its value is -sqrt(3/2).

Is there an error in this question or solution?
In the Following, Determine Whether the Given Quadratic Equation Have Real Roots and If So, Find the Roots: 2x^2-2sqrt6x+3=0 Concept: Relationship Between Discriminant and Nature of Roots.