# Rajesh donated some money and books to a school for poor children. Money and books can be represented by the zeroes (i.e alpha, beta) of the polynomial p(x) = 2x2- 5x 7. Akshitawho is friend of Rajesh, also got inspired by him and donated the money and books in the form of a polynomial whose zeroes are 2alpha 3beta and 3alpha 2beta. Find the polynomial whose zeroes are 2alpha 3beta and 3alpha 2beta. Why did Akshitagot inspired by Rajesh?

1
by anandhusuresh22

2015-10-05T16:33:22+05:30

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There seems to be some mistake in the given polynomial  p(x).

p(x) = 2 x² - 5 x - 7             if it is +7 then the roots are imaginary.
roots are  :   α+β = 5/2  and  αβ = 7/2
α , β = [5 +- √(25+56)]/4 =    -1  or  7/2

But the number of books or Money cannot be negative... So probably Rajesh give some money and took some books from the school or,  he gave some books to the school and took money from the school.  Probably that is what inspired them.

let α = -1      β = 7/2

Polynomial with roots: 2α and 3β is:  x² - (2α+3β) x + (2α)(3β)
= 2 x² - 17x - 42
Polynomial with roots : 3α and 2β is:  x² - (3α+2β) x + (2β)(3α)
= x² - 4 x - 21
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