Question

solve it with correct answer​

Answer 1

Step-by-step explanation:

Given :-

x²+2√3x-24

To find :-

Solve the expression ?

Solution:-

Given polynomial is x²+2√3x-24

24 can be written as

24 = 2×2×2×3

24 = 2×2×2×√3×√3

24 = 4√3×2√3

x²+2√3x-(4√3×2√3)

=> x²+4√3x-2√3x-(4√3×2√3)

=> x(x+4√3) -2√3(x+4√3)

=> (x+4√3)(x-2√3)

The factorization of x²+2√3x-24 is (x+4√3)(x-2√3)

To get zeroes we write the polynomial is equal to zero.

=>(x+4√3)(x-2√3)=0

=> x+4√3 = 0 or x-2√3 = 0

=> x = -4√3 or x = 2√3

Answer:-

Zeroes of the given polynomial are -4√3 and 2√3

Used Method :-

• Splitting the middle term

Answer 2

Answer:

Step-by-step explanation:

Given,

let p ( x ) = x ^2 + 2√3 x - 24 = 0

Comparing the given polinomial with ax square + bx + c = 0 , we have

a = 1 , b = 2√3 and c = -24

∴ x = -b ± √ b square - 4ac / 2a

= - 2√3 ± √ (2√3) whole square - 4 × 1 × ( - 24 ) / 2 × 1

= - 2√3 ± √ 12 + 96 / 2 [∵(2√3)whole square = 2 square × (√3) whole square = 4 × 3 = 12 .Here whole square and root are cancelled .] (∵ - × - = + )

= - 2√3 ± √108 / 2

= - 2√3 ± √ ( 2 ×2 × 3 × 3 ×3) / 2

= - 2√3 ± [ ( √ (2) square ) × ( √3 square ) × √3 ] / 2

= - 2√3 ± [ 2 × 3 × √3 ] / 2

= - 2√3 ± (6√3) / 2

= (- 2√3 + 6√3 ) / 2 or (-2√3 - 6√3 ) / 2

= 4√3 / 2 or - 8√3 / 2

= 2√3 or - 4√3 is the answer.