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In the Following, Determine Whether the Given Quadratic Equation Have Real Roots and If So, Find the Roots: `Sqrt3x^2+10x-8sqrt3=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:

`sqrt3x^2+10x-8sqrt3=0`

Solution

We have been given, `sqrt3x^2+10x-8sqrt3=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=sqrt3`, b = 10 and `c=-8sqrt3`.

Therefore, the discriminant is given as,

`D=(10)^2-4(sqrt3)(-8sqrt3)`

= 100 + 96

= 196

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=(-(10)+-sqrt196)/(2(sqrt3))`

`=(-10+-14)/(2sqrt3)`

`=(-5+-7)/sqrt3`

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

`x=(-5+7)/sqrt3`

`=2/sqrt3`

Also,

`x=(-5-7)/sqrt3`

`=-4sqrt3`

Therefore, the roots of the equation are `2/sqrt3` and `-4sqrt3`.

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APPEARS IN

 RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 4: Quadratic Equations
Ex. 4.5 | Q: 2.03 | Page no. 32
 RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 4: Quadratic Equations
Ex. 4.5 | Q: 2.03 | Page no. 32
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In the Following, Determine Whether the Given Quadratic Equation Have Real Roots and If So, Find the Roots: `Sqrt3x^2+10x-8sqrt3=0` Concept: Relationship Between Discriminant and Nature of Roots.
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