Question

solve 4√3x²+5x-2√3=0 by facyorization method​

Answer 1

Solution:-

Given equation is

$\rm \to4 \sqrt{3} {x}^{2} + 5x - 2 \sqrt{3} = 0$

Split into middle

$\rm \to \: 4 \sqrt{3} {x}^{2} + 8x - 3x - 2 \sqrt{3} = 0$

$\rm \to \: 4x( \sqrt{3} {x} + 2) - \sqrt{3} ( \sqrt{3} x + 2) = 0$

$\rm \to \: (4x - \sqrt{3} )( \sqrt{3} x + 2) = 0$

$\rm \to \: 4x - \sqrt{3} = 0 \: and \: \sqrt{3} x + 2 = 0$

$\rm \to \: x = \dfrac{ \sqrt{3} }{4} \: and \: x = \dfrac{ - 2}{ \sqrt{3} }$

More about quadratic equation

Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax2 + bx + c where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where ‘a’ is called the leading coefficient and ‘c’ is called the absolute term of f (x). The values of x satisfying the quadratic equation are the roots of the quadratic equation (α,β).

The quadratic equation will always have two roots. The nature of roots may be either real or imaginary.

Answer 2

Answer:

x =  $\frac{\sqrt{3} }{4}, \frac{-2}{\sqrt{3} }$

Step-by-step explanation:

Required to solve the equation 4√3x²+5x-2√3=0

Solution:

To factorize by splitting the middle term

To split the middle term we need to find two numbers such that the sum of the numbers = +5 and the Product of the numbers = 4√3×-2√3 =-24

Hence, the numbers are 8 and (-3) such that 8+(-3) = 5 and 8 ×(-3) = -24

∴ 4√3x²+5x-2√3 =0

⇒ 4√3x²+8x -3x-2√3 = 0

⇒ 4√3x²+8x -√3×√3x-2√3 = 0 (∵3 =√3×√3)

⇒ 4x(√3x+2) - √3(√3x+2) = 0

⇒ (4x-√3)(√3x+2) = 0

⇒ 4x -√3 = 0 or √3x+2 = 0

⇒ x = $\frac{\sqrt{3} }{4}$ or x =$\frac{-2}{\sqrt{3} }$

∴ x =  $\frac{\sqrt{3} }{4}, \frac{-2}{\sqrt{3} }$

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