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# In the Following, Determine Whether the Given Quadratic Equation Have Real Roots and If So, Find the Roots: 3x^2+2sqrt5x-5=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:

3x^2+2sqrt5x-5=0

#### Solution

We have been given, 3x^2+2sqrt5x-5=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=2sqrt5 and c = -5.

Therefore, the discriminant is given as,

D=(2sqrt5)^2-4(3)(-5)

= 20 + 60

= 80

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=(-(2sqrt5)+-sqrt80)/(2(3))

=(-2sqrt5+-4sqrt5)(2(3))

=(-sqrt5+-2sqrt5)/3

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

x=(-sqrt5+2sqrt5)/3

=sqrt5/3

Also,

=(-sqrt5-2sqrt5)/3

=-sqrt5

Therefore, the roots of the equation are sqrt5/3 and -sqrt5.

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#### APPEARS IN

RD Sharma Solution for Class 10 Maths (2018 (Latest))
Solution In the Following, Determine Whether the Given Quadratic Equation Have Real Roots and If So, Find the Roots: 3x^2+2sqrt5x-5=0 Concept: Relationship Between Discriminant and Nature of Roots.