How do you write a polynomial in standard form given zeros 3,-2,1/2?
Given that the zeros of a polynomial are x = a , x = b and x = c.
#(x-a),(x-b)" and " (x-c)" are the factors"#
#y=(x-a)(x-b)(x-c)" is the polynomial"#
Here the zeros are
#x=3,x=-2" and " x=1/2#
#rArr(x-3),(x+2)" and " (x-1/2)" are the factors"#
#rArry=(x-3)(x+2)(x-1/2)" gives the polynomial"#
distribute the first 'pair' of brackets.
distributing and collecting like terms.
#rArry=x^3-3/2x^2-11/2x+3" is the polynomial"#
The desired polynomial is
A polynomial with zeros
Hence a polynomial with zeros
We are given
To find the reqd. Poly., we can use Vieta's Rule, which relates the
zeroes of the Poly. with its co-effs.
Vieta's Rule for Cubic Poly. : If,
zeroes of a Cubic Poly.
In our case, we have, by