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In the Following, Determine Whether the Given Quadratic Equation Have Real Roots and If So, Find the Roots: 3a2x2 + 8abx + 4b2 = 0, A ≠ 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:

3a2x2 + 8abx + 4b2 = 0, a ≠ 0

Solution

We have been given, 3a2x2 + 8abx + 4b2 = 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 = 3a2, b = 8ab and c = 4b2.

Therefore, the discriminant is given as,

D = (8ab)2 - 4(3a2)(4b2)

= 64a2b2 - 48a2b2

= 16a2b2

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=(-(8ab)+-sqrt16a2b2)/(2(3a2))`

`=(-8ab+-4ab)/(6a^2)`

`=(-4b+-2b)/(3a)`

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

`x=(-4b+2b)/(3a)`

`=-(2b)/(3a)`

Also,

`x=(-4b-2b)/(3a)`

`=(-2b)/a`

Therefore, the roots of the equation are `-(2b)/(3a)` and `(-2b)/a`.

  Is there an error in this question or solution?
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APPEARS IN

 RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 4: Quadratic Equations
Ex. 4.5 | Q: 2.06 | Page no. 32
 RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 4: Quadratic Equations
Ex. 4.5 | Q: 2.06 | 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: 3a2x2 + 8abx + 4b2 = 0, A ≠ 0 Concept: Relationship Between Discriminant and Nature of Roots.
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