Rajesh donated some money and books to a school for poor children Money and books can be represented by - Maths - Polynomials

Question

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?

Tanveer Sofi · Accepted Answer

The money and books donated by Rajesh are represented by the zeros i
e
, α & βof the polynomial px=2x2-5x+7Using the relation between roots and coefficients of the polynomial:α+β=-coefficient of xcoefficient of x2=--52=52αβ=constant termcoefficient of x2=72Now, we have to find the polynomial whoose zeros are 2α+3β  and 3α+2β:The equation of the polynomial with roots 2α+3β   and   3α+2β is given by:x2-sum of zerosx+product of zeross=x2-2α+3β+3α+2β x+2α+3β3α+2β=x2-5α+β x +6α2+6β2+13αβ=x2-5α+β x +6α2+β2+2αβ+αβ=x2-5α+β x + 6α+β2+αβ=x2-5×52 x +6522+72                          As, α+β=52 and αβ=72=x2-252x+752+72=x2-252x+822The general form of polynomials with  zeros 2α+3β  and 3α+2β  iskx2-252x+822If k=2,then the polynomial is2x2-25x+82Hence, the  money and books donated by Akshita are represented by the zeros of thepolynomial