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# In the Following, Determine Whether the Given Quadratic Equation Have Real Roots and If So, Find the Roots: 3x2 - 5x + 2 = 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:

3x2 - 5x + 2 = 0

#### Solution

We have been given, 3x2 - 5x + 2 = 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 = 3, b = -5 and c = 2.

Therefore, the discriminant is given as,

D = (-5)2 - 4(3)(2)

= 25 - 24

= 1

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 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=(-(-5)+-sqrt1)/(2(3))

=(5+-1)/6

Now we solve both cases for the two values of x. So, we have,

x=(5+1)/6

=6/6

= 1

Also,

x=(5-1)/6

=4/6

=2/3

Therefore, the roots of the equation are 2/3 and 1.

Is there an error in this question or solution?