Question

find the roots of quadratic equation: 4√3x²+5x-2√3=0

Answer 1

4√3x^2+5x-2√3=0
by middle term splitting method,
4√3x^2+8x-3x-2√3=0
4x(√3x+2)-√3(√3x+2)=0
(4x-√3) and (√3x+2)
4x-√3=0 and √3x+2=0
4x=√3 and √3x=-2
x=√3/4 and x= -2/√3
hope this helps

Answer 2

Given:

A quadratic equation:

4√3x² + 5x - 2√3 = 0

To find:

The roots of the given quadratic equation.

Solution:

The roots of a given quadratic equation are √3/4 and -2/√3.

To answer this question, we will follow the following steps:

As given in the question,

we have a quadratic equation

4√3x² + 5x - 2√3 = 0 (i)

To find the roots of the quadratic equation, we will write the second term i.e. 5x as the sum of those two terms whose product is equal to the product of the first and third term i.e. 4√3x and -2√3x. (product of 4√3 and -2√3 is -24x²)

So,

(i) can be written as

4√3x² + 8x - 3x - 2√3 = 0

4x ( √3x + 2) -√3( √3x + 2) = 0

After taking common factors, we get

( 4x - √3) (√3x + 2) = 0

4x - √3 and √3x + 2 = 0

x = √3/4 and -2/√3

Hence, the two roots of a given quadratic equation are √3/4 and -2/√3.