Math, asked by rishitasharna824, 7 months ago

Find the value of sum of
roots
of given Polynomial 2x²-4x+6​

Answers

Answered by anilmeena9782
1

If α and β are Zeroes of a Quadratic Polynomial, ax² + bx + c then :

● α and β are roots of the Quadratic Equation, ax² + bx + c = 0

● \mathsf{Sum\;of\;the\;Roots\;(\alpha + \beta) = \dfrac{-b}{a}}SumoftheRoots(α+β)=

a

−b

● \mathsf{Product\;of\;the\;Roots\;(\alpha.\beta) = \dfrac{c}{a}}ProductoftheRoots(α.β)=

a

c

Given : α and β are zeros of Quadratic Polynomial 2x² - 4x + 5

Here : a = 2 and b = -4 and c = 5

● α and β are roots of the Quadratic Equation, 2x² - 4x + 5 = 0

● \mathsf{Sum\;of\;the\;Roots\;(\alpha + \beta) = \dfrac{4}{2} = 2}SumoftheRoots(α+β)=

2

4

=2

● \mathsf{Product\;of\;the\;Roots\;(\alpha.\beta) = \dfrac{5}{2}}ProductoftheRoots(α.β)=

2

5

Consider : (α + β)³

:\implies:⟹ (α + β)³ = α³ + 3α²β + 3αβ² + β³

:\implies:⟹ (α + β)³ = α³ + 3αβ(α + β) + β³

:\implies:⟹ α³ + β³ = (α + β)³ - 3αβ(α + β)

\mathsf{\implies \alpha^3 + \beta^3 = 2^3 - 3\bigg(\dfrac{5}{2}\bigg)(2)}⟹α

3

3

=2

3

−3(

2

5

)(2)

\mathsf{\implies \alpha^3 + \beta^3 = 8 - (3\times 5)}⟹α

3

3

=8−(3×5)

\mathsf{\implies \alpha^3 + \beta^3 = 8 - 15}⟹α

3

3

=8−15

\mathsf{\implies \alpha^3 + \beta^3 = -7}⟹α

3

3

=−7

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