Question

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Answer 1

STEP-BY-STEP EXPLANATION:

.

$:\implies\tt {x}^{2} - ( \sqrt{3} +2 )x + 2 \sqrt{3} = 0 \: \: \\ \\ :\implies\tt {x}^{2} - \sqrt{3} x - 2x + 2 \sqrt{3} = 0 \: \: \: \\ \\ :\implies\tt x(x - \sqrt{3} ) - 2(x - \sqrt{3} ) = 0 \\ \\ :\implies\tt (x - 2)(x - \sqrt{3} ) = 0 \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

So,

• The roots are 2 and √3.

VERIFICATION,

$:\implies\tt p(x) = {x}^{2} - ( \sqrt{3} + 2)x + 2 \sqrt{3} \\ \\ :\implies\tt p(2) = {2}^{2} - ( \sqrt{3} + 2)2 + 2 \sqrt{3}$

$:\implies\tt 0 = 4 - 2 \sqrt{3} - 4 + 2\sqrt{3} \\ \\ :\implies\tt 0 = 0 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ :\implies\tt LHS = RHS \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$:\implies\tt p( \sqrt{3} ) = {( \sqrt{3}) }^{2} - ( \sqrt{3} + 2) \sqrt{3} + 2 \sqrt{3} \\ \\ :\implies\tt 0 = 3 - 3 - 2 \sqrt{3} + 2 \sqrt{3} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$:\implies\tt 0 = 0 \: \: \: \: \: \: \: \: \: \\ \\ :\implies\tt LHS = RHS$

Answer 2

Step-by-step explanation:

refer to the attachment.

it's Isha

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