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3 years ago

8

Hi, i need to calculate roots x1 and x2 using the vieta theorem, can anyone help me? I have found the answer for x1 and x2, its

1,5 and 2, all i need is a solution on how to get this answer, the equation is in the picture, will give you brainliest if you type down the correct solution for me, thanks.

1 answer:

stellarik [79]3 years ago

7 0

Answer:

Solution given:

-2x²+7x-6=0

2x²-7x+6=0

Comparing above equation with ax²+bx+c

we get

a=2

b=-7

c=6

By using Vieta's theorem

X1+X2= $\frac{-b}{a}$ = $\frac{7}{2}$

again

X1X2= $\frac{c}{a}$ = $\frac{6}{2}$ =3

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${\large{\textsf{\textbf{\underline{\underline{Given :}}}}}}$

★ Sanya has a piece of land which is in the shape of a rhombus.

★ She wants her one daughter and one son to work on the land and produce different crops, for which she divides the land in two equal parts.

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★ One of the diagonal = 160 m.

${\large{\textsf{\textbf{\underline{\underline{To \: Find :}}}}}}$

★ Area each of them [son and daughter] will get.

${\large{\textsf{\textbf{\underline{\underline{Solution :}}}}}}$

Let, ABCD be the rhombus shaped field and each side of the field be $x$

[ All sides of the rhombus are equal, therefore we will let the each side of the field be $x$ ]

Now,

• Perimeter = 400m

$\longrightarrow \tt AB+BC+CD+AD=400m$

$\longrightarrow \tt x + x + x + x=400$

$\longrightarrow \tt 4x=400$

$\longrightarrow \tt \: x = \dfrac{400}{4}$

$\longrightarrow \tt x= \red{100m}$

$\therefore$ Each side of the field = <u>100m</u><u>.</u>

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So, For $\triangle$ ABD,

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• b = 100 [AD]

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$\therefore \tt Simi \: perimeter \: [S] = \boxed{ \sf \dfrac{a + b + c}{2} }$

$\longrightarrow \tt S = \dfrac{100 + 100 + 160}{2}$

$\longrightarrow \tt S = \cancel{ \dfrac{360}{2}}$

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Using <u>herons formula</u><u>,</u>

$\star \tt Area \: of \: \triangle = \boxed{\bf{{ \sqrt{s(s - a)(s - b)(s - c) } }}} \star$

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• s is the simi perimeter = 180m

• a, b and c are sides of the triangle which are 100m, 100m and 160m respectively.

<u>Putt</u><u>ing</u><u> the</u><u> values</u><u>,</u>

$\longrightarrow \tt Area_{ ( \triangle \: ABD)} = \tt \sqrt{180(180 - 100)(180 - 100)(180 - 160) }$

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$\longrightarrow \tt Area_{ ( \triangle \: ABD)} = 3 \times 20 \times 80$

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Thus, area of $\triangle$ ABD = <u>4800 m²</u>

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Area of $\triangle$ BCD = 4800 m²

<u>Therefore, area each of them [son and daughter] will get = 4800 m²</u>

${\large{\textsf{\textbf{\underline{\underline{Note :}}}}}}$

★ Figure in attachment.

${\underline{\rule{290pt}{2pt}}}$

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