If alpha and beta are zeroes if the polynomial 2x²-7x+5 then find a polynomial whose zeroes are 2 alpha + 1 and 2 beta+ 3 ??

Question

6036 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-02-21T09:13:44

# x^2-11x+30#.

Let, the poly. be #p(x)=2x^2-7x+5#.

Then, #p(x)=0 rArr 2x^2-7x+5=0#.

#:. ul(2x^2-5x)-ul(2x+5)=0#.

#:. x(2x-5)-1(2x-5)=0#.

#:. (2x-5)(x-1)=0#.

#:." The zeroes of "p(x)" are "5/2, and, 1#.

We select, #alpha=5/2 and beta=1#.

Letting #alpha_0=2alpha+1, and beta_0=2beta+3#, we have,

#alpha_0=2(5/2)+1=6, and beta_0=2(1)+3=5#.

#:. alpha_0+beta_0=6+5=11, and alpha_0*beta_0=6*5=30#.

So, the desired poly. #P(x)# with these zeroes is given by,

#P(x)=x^2-(alpha_0+beta_0)x+alpha_0*beta_0, i.e., #

#P(x)=x^2-11x+30#.