The roots of the polynomial f(x)=7x2+31x+c=0 are reciprocals of each other. What is the value of c?
we know the discriminant d^2 = 961-28c
so, the roots are
(-31 + √(961-28c))/14
and
(-31 - √(961-28c))/14
since they are reciprocals,
(-31 - √(961-28c))/14 = 14/(-31 + √(961-28c))
961-(961-28c) = 196
c = 7
3(x+6)+8x=
To find the value of c, we need to use the fact that the roots of the polynomial are reciprocals of each other. Let's start by finding the roots of the polynomial.
A polynomial of the form ax^2 + bx + c = 0 can be solved using the quadratic formula: (-b ± √(b^2 - 4ac)) / (2a).
In this case, the polynomial f(x) = 7x^2 + 31x + c = 0. So, a = 7, b = 31, and c is the value we are trying to find.
Since the roots are reciprocals of each other, let's assume the roots are r and 1/r.
Applying the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
x = (-31 ± √(31^2 - 4 * 7 * c)) / (2 * 7)
The roots of f(x) are the values of x that make f(x) equal to zero. Therefore, we can set the discriminant (b^2 - 4ac) to zero, as we want to find the value of c that satisfies this condition.
b^2 - 4ac = 0
(31^2) - 4(7)(c) = 0
961 - 28c = 0
28c = 961
c = 961 / 28
So, the value of c is 961 / 28.