Question

If α and β are zeroes of polynomial p(x) = x2-5x+6 then find the value of α - β+3αβ​

Answer 1

$\textbf{Given:}$

$\mathrm{\alpha}\;\text{and}\;\mathrm{\beta}\;\text{are zeros of}$

$\mathrm{P(x)=x^2-5x+6}$

$\textbf{To find:}$

$\text{The value of}$

$\mathrm{\alpha-\beta+3\alpha\beta}$

$\textbf{Solution:}$

$\text{Consider,}$

$\mathrm{P(x)=x^2-5x+6}$

$\mathrm{\alpha+\beta=5}$

$\mathrm{\alpha\,\beta=6}$

$\mathrm{(\alpha-\beta)^2=(\alpha+\beta)^2-4\,\alpha\,\beta}$

$\mathrm{(\alpha-\beta)^2=(5)^2-4(6)}$

$\mathrm{(\alpha-\beta)^2=25-24}$

$\mathrm{(\alpha-\beta)^2=1}$

$\mathrm{\alpha-\beta=1}$

$\text{Now}$

$\mathrm{(\alpha-\beta)+3\alpha\beta}$

$\mathrm{=1+3(6)}$

$\mathrm{=1+18}$

$\mathrm{=19}$

$\textbf{Answer:}$

$\text{The value of}$

$\mathrm{\alpha-\beta+3\alpha\beta=19}$

$\textbf{Find more:}$

1)If alpha and beta are zeroes of quadratic polynomial x2 -(k+6x)+2(2k-1) 

find k if alpha +beta=1/2alpha beta 

2)If alpha and beta are zeroes of x2-6x+a, find the value of a if 3alpha+2beta=20

https://brainly.in/question/16419985

3)If α and β are the zeroes of the polynomial

xsquare+ x – 1, the evaluate α + β + αβ

https://brainly.in/question/17511372

Answer 2

Step-by-step explanation:

iven:

\mathrm{\alpha}\;\text{and}\;\mathrm{\beta}\;\text{are zeros of}αandβare zeros of

\mathrm{P(x)=x^2-5x+6}P(x)=x

2

−5x+6

\textbf{To find:}To find:

\text{The value of}The value of

\mathrm{\alpha-\beta+3\alpha\beta}α−β+3αβ

\textbf{Solution:}Solution:

\text{Consider,}Consider,

\mathrm{P(x)=x^2-5x+6}P(x)=x

2

−5x+6

\mathrm{\alpha+\beta=5}α+β=5

\mathrm{\alpha\,\beta=6}αβ=6

\mathrm{(\alpha-\beta)^2=(\alpha+\beta)^2-4\,\alpha\,\beta}(α−β)

2

=(α+β)

2

−4αβ

\mathrm{(\alpha-\beta)^2=(5)^2-4(6)}(α−β)

2

=(5)

2

−4(6)

\mathrm{(\alpha-\beta)^2=25-24}(α−β)

2

=25−24

\mathrm{(\alpha-\beta)^2=1}(α−β)

2

=1

\mathrm{\alpha-\beta=1}α−β=1

\text{Now}Now

\mathrm{(\alpha-\beta)+3\alpha\beta}(α−β)+3αβ

\mathrm{=1+3(6)}=1+3(6)

\mathrm{=1+18}=1+18

\mathrm{=19}=19

\textbf{Answer:}Answer:

\text{The value of}The value of

\mathrm{\alpha-\beta+3\alpha\beta=19}α−β+3αβ=19