Question

Find the roots of the following quadratic equations by factorisation: √3x2 + 10x + 7√3 = 0

Answer 1

Answer:

Roots of the given equation are $- \sqrt{3} \: and \: - \frac{7}{ \sqrt{3} }$

Step-by-step explanation:

$= > \sqrt{3} {x}^{2} + 10x + 7 \sqrt{3} = 0 \\ \\ = > \sqrt{3} {x}^{2} + (7 + 3)x + 7 \sqrt{3} = 0 \\ \\ = > \sqrt{3} {x}^{2} + 7x + 3x + 7 \sqrt{3} = 0 \\ \\ = > x( \sqrt{3} x + 7) \sqrt{3} ( \sqrt{3} x + 7) = 0 \\ \\ = > (x + \sqrt{3} )( \sqrt{3} x + 7) = 0 \\ \\ = > (x + \sqrt{3} ) = 0 \: \: \: \: \: and( \sqrt{3} x + 7) = 0 \\ \\ = > x = - \sqrt{3} \: \: \: \: \: and \: \: \: \: \: x = - \frac{7}{ \sqrt{3} }$

Answer 2

Answer:

$\boxed{ \bold{ \frac{ - 7}{ \sqrt{3} }\: and \: - \sqrt{3} \: are \: zeros \: of \: polynomial} }$

Step by step explanation:

To Find:

the roots of the √3x2 + 10x + 7√3 = 0 quadratic equations by factorisation.

Solution:

$\sf\sqrt{3} {x}^{2} + 10x + 7 \sqrt{3} = 0 \\ \\ \sf \sqrt{3} {x}^{2} + 7x + 3x + 7 \sqrt{3} = 0 \\ \\ \sf x( \sqrt{3} x + 7) + \sqrt{3} ( \sqrt{3} x + 7 = 0 \\ \\ \sf ( \sqrt{3} x + 7) \: (x + \sqrt{3} ) = 0 \\ \\ \: \sf \: \implies \: \sqrt{3} x + 7 = 0 \\ \\ \sf \: \implies\sqrt{3} x = \: - 7 \\ \\ \\ \: \: \: \: \: \: \: \boxed {\bold{ \ \: x = \frac{7}{ \sqrt{3} }}} \\ \\ \implies \sf \: x + \sqrt{3} = 0 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \boxed {\bold{ x = - \sqrt{3}} }$