Please explain how to solve the following problems.
1.what do you understand by the value of a polynomial at a given point?
2. find the quadratic polymomial whose one zeroes 2+ROOTof 3
(1) Value of a given polynomial at a given point means value of that polynomial at a particular value of the given variable. Suppose, if the given polynomial is f(x) = 3x3 + 5x2 + 6x + 8, then value of f(x) at a point x = 3 is f(3) = 3(3)3 + 5(3)2 + 6(3) + 8 = 81 + 45 + 18 + 8 = 152
(2) One zero of the polynomial equation =
Then, the other zero =
Sum of the polynomials,
Product of the polynomials,
Hence, required polynomial,
x2 – (Sum of the polynomials)x + (product of the polynomials) = 0
x2 – 4x + 1 = 0