Edit the following sentence
Reena and me went to the market
Answers
Explanation:
\large \bf \clubs \: Given :-♣ Given :−
α and β are the roots of the equation
x² + 5x + 5 =0
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\large \bf \clubs \: To \: Find :-♣ To Find:−
• The Equation whose roots are (α + 1) and (β + 1).
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\large \bf \clubs \: Main \: Concepts :-♣ Main Concepts:−
1》 For a qudratic Equation of the Form ax² + bx + c = 0
Sum of Roots = \sf-\dfrac{b}{a} −
a
b
Product of Roots = \sf\dfrac{c}{a}
a
c
2》 A Quadratic Equation whose sum and product of Roots are S and P respectively is given by x² - Sx + P = 0
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\large \bf \clubs \: Solution :-♣ Solution:−
As α and β are the roots of the equation
x² + 5x + 5 =0
Hence ,
\begin{gathered} \pmb{ \alpha + \beta = - 5 } \: \: - - - - (1)\\ \bf and \\ \pmb{ \alpha \beta = 5} \: \: - - - - (2)\end{gathered}
α + β =−5
α + β =−5 − − − −(1)
and
α β =5
α β =5 − − − −(2)
For The Equation whose Roots are
(α + 1) and (β + 1).
\begin{gathered} \sf S um \: of \: Roots = S \\ \\ = \sf \alpha + 1 + \beta + 1 \\ \\ = \alpha + \beta + 2 \\ \\ \bf \: \: \: \{using \: \: (1) \} \\ \\ \sf S = - 5 + 2\\ \\ \large:\longmapsto \boxed{\pmb{\boxed{S = - 3}}}\end{gathered}
Sum of Roots =S
=α +1+ β +1
= α + β +2
{using (1) }
S= −5+2
:⟼
S= −3
S= −3
\begin{gathered} \sf P roduct \: of \: Roots = P \\ \\ = ( \alpha + 1)( \beta + 1) \\ \\ = \alpha \beta + \alpha + \beta + 1 \\ \\ \bf \: \: \: \{using \: (1) \: and \: (2) \} \\ \\ \sf P = 5 - 5 + 1 \\ \\ \large :\longmapsto\boxed{ \pmb{ \boxed{P = 1}}}\end{gathered}
Product of Roots =P
=(α +1)(β +1)
= α β + α + β +1
{using (1)and(2)}
P=5−5+1
:⟼
P=1
P=1
Hence The Equation whose Roots are
(α + 1) and (β + 1) will be x² - Sx + P = 0
Where S and P are Sum and Product of roots.
That is ,
The Required Equation is
x² - ( - 3) x + 1 =0
\large \pink{ : \longmapsto \bf {x}^{2} + 3x + 1 = 0 }:⟼ x
2
+3x+1=0
\begin{gathered} \LARGE\red{\mathfrak{ \text{W}hich \:\:is\:\: the\:\: required} }\\ \Huge \red{\mathfrak{ \text{ A}nswer.}}\end{gathered}
Whichistherequired
Answer.
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Answer:
Reena and I went to the market