A one-variable polynomial is an arithmetic expression of the form a0 + a1x + a2x2 + ...+ akxk The highest exponent, , is called the degree of the polynomial, and the constants a0, a1, ...ak, are the coefficients. For example, here are two polynomials of degree 3:

2.1 + 4.8 x + 0.1 x2 + (-7.1) x3

2.9 + 0.8 x + 10.1 x2 + 1.7 x3

Design a C++ class for polynomials. Your class should implement a constructor that accepts a vector of numbers and initializes the polynomial using it. The array contains the constants a0, a1, ...ak, in that specific order. In addition, your class should implement the following methods:

add(p) which adds another polynomial p and returns the resultant polynomial

subtract(p) which subtracts another polynomial p and returns the resultant polynomial

multiply(p) which multiplies the polynomial by another polynomial p, and returns the resultant polynomial

display() which displays the polynomial evaluate(double x) which evaluates the polynomial given a value for x, and returns the result

findRoots() which, if the polynomial is of degree 2 or less, finds and prints the roots.

Your main () should be a test for your polynomial. I will test your program using my own main, which might look like:

int main (){ vector array1 {5, 0, 3.5, 16, -2};

vector array2 {1, -2, 0.5};

polynomial P1 (array1);

polynomial P2 (array2);

polynomial newP = P1.add (P2);

newP.display();

P2.findRoots();

cout << the value of the polynomial is" << newP.evaluate(5) << endl; }

please test the polynomial using both main (). Thanks