Question

factorise 4 root 3 X square + 5 x minus 2 root 3

Answer 1

For middle term splitting :-

firstly multiply the coefficient of x² to the constant term

Here, 4√3 × 2√3 = 24

Now
we have to split 24 as to get 5 either by subtracting or by adding.

=> 4√3x² + 5x - 2√3

4√3 x² + 8x - 3x - 2√3

4x ( √3x + 2 ) - √3 ( √3x + 2 )

( 4x - √3 ) ( √3x + 2 )

Answer 2

Concept:

We need the concept of polynomials.

Polynomial is the form of an expression with constants as real numbers and powers of variable x.

Formula required:

Quadratic formula: -b±√b²-4ac/2a

we find the roots and write them in the factorised form:(x-α)(x-β) where α and β are the roots.

Given:

We are given a polynomial of degree 2

To find:

We are asked to factorise the given polynomial

Solution:

The polynomial is given as  4√3x²+5x-2√3

We first find the roots of the polynomial.

To find the roots we have the equation as :

4√3x²+5x-2√3=0.........................(1)

Since the polynomial is of degree 2, we will get two roots.

We use the quadratic formula to find the roots:

-b±√b²-4ac/2a where a is the co-efficient of x² and b is the co-efficient and c is the constant.

From Eqn(1): a=4√3, b=5 and c=-2√3

Let α and β be the roots

then, from the quadratic formula

=-5±√5²-4x4√3x(-2√3)/2x4√3

=-5±√25+32x3/8√3

Taking the plus and minus parts separately,

for plus part:

α=$\frac{-5+\sqrt{25+32X3} }{8\sqrt{3} }$

  =$\frac{-5+\sqrt{25+96} }{8\sqrt{3} }$

   =$\frac{-5+\sqrt{121} }{8\sqrt{3} }$

   =$\frac{-5+11}{8\sqrt{3} }$

    =$\frac{6}{8\sqrt{3} }$

 α=$\frac{3}{4\sqrt{3} }$

For minus part:

β=$\frac{-5-\sqrt{25+32X3} }{8\sqrt{3} }$

 =$\frac{-5-\sqrt{121} }{8\sqrt{3} }$

 =-5-11/8√3

 =-16/8√3

 β=-2/√3

Hence, with these roots we can write the factorised form as:

(x-3/4√3)(x+2/√3)