Question

V3x-2/2x-2/3 = 0 by splitting the middle term

Answer 1

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your answer on my attachment

hope helped

Answer 2

$\huge\mathfrak\blue{Answer:}$

Given:

• We have been given a Quadratic Polynomial as :

• $\sf{\sqrt{3 \:}x^2 - 2 \sqrt{2 \: }x - 2 \sqrt{3 \: }}$

To Find:

• We have to find the roots of given Quadratic Polynomial using middle term splitting method

Concept Used:

$\large\underline{\sf{\orange{Middle \: Term \: Splitting \: Method }}}$

In this method middle term of the equation is broken down in its two factor such that their product is equal to the Product of First and last term

Solution:

Given a Quadratic Polynomial

$\boxed{\sf{\sqrt{3 \:}x^2 - 2 \sqrt{2 \: }x - 2 \sqrt{3 \: } = 0}}$

Multiplying Coefficient of x² with constant

• $\sf{\sqrt{3 \: } \times 2 \sqrt{3 \:}}$
• $\sf{3 \times 2}$
• 6

We need to find two numbers whose multiplication is 6 and difference is $\sf{2 \sqrt{2 \:}}$

Two such numbers are $3 \sqrt{2 \:}$ and $\sqrt{2 \:}$

Middle Term Splitting in Polynomial

➬$\: \sf{\sqrt{3 \:}x^2 - 3\sqrt{2 \: }x +\sqrt{2 \: }x - 2 \sqrt{3 \: } = 0}$

➬$\: \sf{\sqrt{3 \:}x \: ( \: x - \sqrt{6 \: } \: ) +\sqrt{2 \: } \: ( \: x - \sqrt{6 \: }) = 0}$

➬$\: \sf{( \: x - \sqrt{6 \: } \: ) \: ( \: \sqrt{3 \:}x + \sqrt{2 \: } \: ) = 0}$

$\sf{ }$

As the product of two terms is zero

$\odot \:$ Either

$\implies \sf{x - \sqrt{6 \: } = 0} \implies \boxed{\sf{x = \sqrt{6 \:}}}$

$\odot \:$ Or

$\implies \sf{\sqrt{3 \:}x + \sqrt{2 \: } = 0 }$

$\implies \boxed{\sf{ x = - \sqrt{\dfrac{2}{3} \: }}}$

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$\huge\underline{\sf{\red{A}\orange{n}\green{s}\pink{w}\blue{e}\purple{r}}}$

Roots of Equation are $\sf{\sqrt{6 \:}}$ and $\sf{\left ( - \sqrt{\dfrac{2}{3} \: } \right ) }$

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$\large\purple{\underline{\underline{\sf{Extra \: Information:}}}}$

• Roots of an equation are the values of x for which the value of given polynomial becomes zero
• Method of Finding roots

• Middle Term Splitting method
• Completing Square method
• Cross multiplication method