Math, asked by daris52, 1 month ago

To help a poor student, ariv donated α pens and β books to him, where α and β represent the zeroes of polynomial x^2-5x + 4. inspired by the deed of ariv,arya also donated 2α+ 3β pens and 3α + 2β books to that student. find a polynomial whose zeroes are the number of pens and books donated by arya. explain why arya got inspired by the deed of ariv.​

Answers

Answered by hukam0685
4

Step-by-step explanation:

Given:To help a poor student, ariv donated α pens and β books to him, where α and β represent the zeroes of polynomial x²-5x + 4. inspired by the deed of ariv,arya also donated 2α+ 3β pens and 3α + 2β books to that student.

To find: find a polynomial whose zeroes are the number of pens and books donated by arya. explain why arya got inspired by the deed of ariv.

Solution:

As \alpha and \beta are zeros of x^2-5x+4

Find zeros of polynomial:

 {x}^{2}  - 4x - x + 4 \\  \\ =  >  x(x - 4) - 1(x - 4) \\  \\  =  > (x - 1)(x - 4) \\

Thus,zeros of polynomial are

x - 1 = 0 \\  \\ x = 1 \\  \\

and

x - 4 = 0 \\  \\ x = 4 \\  \\

let say

 \alpha  = 1 \\  \\  \beta  = 4 \\

ATQ,

Arya donated 2\alpha+3\beta pens

and 3\alpha+2\beta books.

let

\bold{\green{m=2\alpha+3\beta}}

\bold{\pink{n=3\alpha+2\beta}}

Quadratic polynomial with zeros m and n is given by

\bold{ {x}^{2}  - (m + n)x + mn} \\

Find Value of m+n:

Put the value of \alpha and \beta

m + n = 2 \alpha  + 3 \beta  + 3 \alpha  + 2 \beta  \\  \\ m + n = 5 \alpha  + 5 \beta  \\  \\ m + n = 5 (1 +4)  \\  \\ \bold{m + n = 25}...eq3\\\\

Find mn:

mn = (2 \alpha  + 3 \beta )(3 \alpha  + 2 \beta ) \\  \\ mn = (2\times 1+3\times 4)( 3\times 1+2\times 4) \\  \\mn=(2+12)(3+8)\\\\mn=(14)(11)\\\\\bold{mn=154}...eq4\\\\

Therefore, quadratic polynomial is

 {x}^{2}  - 25x + 154 \\  \\

Final answer:

The quadratic polynomial is

 \bold{\purple{{x}^{2}  - 25x + 154}} \\  \\

Arya got inspired by the deed of ariv because helping poor students is a good behavior.

Hope it helps you.

To learn more on brainly:

1) Quadratic polynomial 2x²-3x+1 has zeros as alpha and beta now form a quadratic polynomial whose zeroes are 3alpha and 3b...

https://brainly.in/question/4403481

2)If x + 2a is a factory of x5 - 4a2 + 2x + 2a +3, find a

https://brainly.in/question/42054652

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