Write a poem and try to include these words in it flop,hop,top,mop and stop
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Answer:
Explanation:
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Answer:
⠀▪︎ ⠀Find the discriminant of the quadratic equation 2x² -4x + 3 =0 and the hence find the nature of its roots.
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⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀☆GIVEN QUADRATIC EQUATION : 2x² - 4x + 3 = 0 ,
⠀⠀⠀⠀⠀Now ,
⠀⠀By Comparing it with standard form of QUADRATIC EQUATION and it's given by :
\begin{gathered}\qquad \dag\:\:\bigg\lgroup \sf{ Standard \:_{(QUADRATIC\:EQUATION \:)}\:\:: ax^2 + bx + c \:}\bigg\rgroup \\\\\end{gathered}
†
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Standard
(QUADRATICEQUATION)
:ax
2
+bx+c
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⠀⠀⠀⠀⠀We get ,
⠀⠀⠀⠀⠀▪︎ ⠀a = 2
⠀⠀⠀⠀⠀▪︎ ⠀b = -4
⠀⠀⠀⠀⠀▪︎ ⠀c = 3
\begin{gathered}\dag\:\:\sf{ As,\:We\:know\:that\::}\\\\ \bigstar\:\:\bf Formula\:of\:Discriminant\:: \\\\ \end{gathered}
†As,Weknowthat:
★FormulaofDiscriminant:
\begin{gathered}\qquad \dag\:\:\bigg\lgroup \sf{ D \: = \: b^2 \:-\:4ac }\bigg\rgroup \\\\\end{gathered}
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D=b
2
−4ac
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⠀⠀⠀⠀⠀Here , D is the Discriminant .
⠀⠀⠀⠀⠀&
⠀⠀⠀⠀⠀▪︎ ⠀If D = 0 then The roots are equal , real & rational .
⠀⠀⠀⠀⠀▪︎ ⠀If D > 0 then The roots are real , distinct & rational .
⠀⠀⠀⠀⠀▪︎ ⠀If D < 0 then The roots are imaginary & unequal.
\begin{gathered}\qquad:\implies \sf D \: = \: b^2 \:-\:4ac \:\\\end{gathered}
:⟹D=b
2
−4ac
⠀⠀⠀⠀⠀⠀\begin{gathered}\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}\\\end{gathered}
⋆NowBySubstitutingtheknownValues:
\begin{gathered}\qquad:\implies \sf D \: = \: b^2 \:-\:4ac \:\\\end{gathered}
:⟹D=b
2
−4ac
\begin{gathered}\qquad:\implies \sf D \: = \: (-4)^2 \:-\:4(2)(3) \:\\\end{gathered}
:⟹D=(−4)
2
−4(2)(3)
\begin{gathered}\qquad:\implies \sf D \: = \: 16 \:-\:4(2)(3) \:\\\end{gathered}
:⟹D=16−4(2)(3)
\begin{gathered}\qquad:\implies \sf D \: = \: 16 \:-\:8(3) \:\\\end{gathered}
:⟹D=16−8(3)
\begin{gathered}\qquad:\implies \sf D \: = \: 16 \:-\:24 \:\\\end{gathered}
:⟹D=16−24
\begin{gathered}\qquad:\implies \bf D \: = \: -8 \:\\\end{gathered}
:⟹D=−8
⠀⠀⠀⠀⠀Therefore,
\begin{gathered}\qquad:\implies \bf \: -8 \ < 0 \:\\\end{gathered}
:⟹−8 <0
\begin{gathered}\qquad:\implies \bf D \: \ < \: 0\:\\\end{gathered}
:⟹D <0
\begin{gathered}\qquad :\implies \pmb{\underline{\purple{\: D \: \ < \: 0\: }} }\:\:\bigstar \\\end{gathered}
:⟹
D <0
D <0
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Therefore,
⠀⠀⠀⠀⠀▪︎ ⠀The roots are imaginary & unequal.
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⠀⠀⠀⠀⠀\begin{gathered}\large {\boxed{\sf{\mid{\overline {\underline {\star More\:To\:know\::}}}\mid}}}\\\\\end{gathered}
∣
⋆MoreToknow:
∣
\begin{gathered}\qquad \qquad \boxed {\begin{array}{cc} \bf{\underline {\bigstar\:\: For \: a \:Quadratic \:Polynomial \::}}\\\\ \sf{ Whose \:\:zeroes \:\:are\:\:\alpha \:\&\;\: \beta\:\:} \\\\ 1)\:\: \alpha + \beta \: =\:\dfrac{-b}{a} \quad \bigg\lgroup \bf Sum\:of\;Zeroes \bigg\rgroup \\\\ 2)\:\: \alpha \times \beta \: =\:\dfrac{c}{a} \quad \bigg\lgroup \bf Product \:of\;Zeroes \bigg\rgroup \\\\ \end{array}} \end{gathered}
★ForaQuadraticPolynomial:
Whosezeroesareα&β
1)α+β=
a
−b
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SumofZeroes
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2)α×β=
a
c
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ProductofZeroes
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