Question

Middle term split
root3x^2 + 10x + 7root3

Answer 1

Sum = 10

Product = √3 × 7√3 = 7(√3)^2 = 7×3 = 21

Two numbers with sum as 10 and product as 21 are 7 and 3.

Factorisation -

$\sqrt{3} {x}^{2} + 10x + 7 \sqrt{3} \\ \\ \sqrt{3} {x}^{2} + (7 + 3)x + 7 \sqrt{3} \\ \\ \sqrt{3} {x}^{2} + 7x + 3x + 7 \sqrt{3} \\ \\ \sqrt{3} {x}^{2} + 7x + ( \sqrt{3} {)}^{2} x + 7 \sqrt{3} \\ \\ x( \sqrt{3} x + 7) + \sqrt{3} ( \sqrt{3} x + 7) \\ \\ (x + \sqrt{3} )( \sqrt{3} x + 7)$

Answer 2

Please see the attached document for the answer...

Ignore my bad handwriting....

ANSWER:

$(\sqrt{3} x + 7)(x + \sqrt{3} )$