Question

find the value of x if 4 root 3 X square + 5 x minus 2 root 3 is equal to zero​

Answer 1

Step-by-step explanation:

given quadratic

4√3x²+5x-2√3=0

by spiltting we get

4√3x²+8x-3x-2√3=0

4x(√3x+2)-√3(√3x+2)=0

(4x-√3)(√3x+2)=0

we get

(4x-√3)=0 or (√3x+2)=0

we get

x=√3/4 or x=-2/√3

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Answer 2

Answer:

Step-by-step explanation:

Given

4√3x² + 5x - 2√3 = 0

Given expression is a quadratic in terms of x.

By splitting the middle term method, we get

4√3x² + 5x - 2√3 = 0

⇒ 4√3x² + 8x - 3x - 2√3 = 0

⇒ 4x(√3x + 2) -√3(√3x + 2) = 0

⇒ (4x - √3)(√3x + 2) = 0

So, either 4x - √3 = 0 or √3x + 2 = 0

⇒ 4x = √3 or √3x = -2

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

(-2/√3, when rationalised = -2√3/3)

$\rule{200}{2}$

What is splitting the middle term method?

Consider a quadratic ax² + bx + c. While splitting it into two terms, say y and z we split it in such a way that

ac = yz

and, y + z = b

In the question given we had a = 4√3, b = 5 and c = - 2√3

ac = 4√3 × (- 2√3) = (- 24)

and b = 5

So, had split it in y and z in such a way that y + z = b and yz = ac

We had 8 and -3 suitable for the condition, so we had splitted the middle term 5x as 8x - 3x.