By concepts of polynomials and systems of linear equations, the constants c and d of the expression p(x) = x⁴ - 5 · x³ - 7 · x² + c · x + d are 29 and 30.
<h3>How to determine the missing coefficients of a quartic equation</h3>
A value x is a root of a polynomial if and only if p(x) = 0. We must replace the given equation with the given roots and solve the resulting system of <em>linear</em> equations:
(- 1)⁴ - 5 · (- 1)³ - 7 · (- 1)² + (- 1) · c + d = 0
- c + d = 1 (1)
3⁴ - 5 · 3³ - 7 · 3² + 3 · c + d = 0
3 · c + d = 117 (2)
The solution of this system is c = 29 and d = 30.
By concepts of polynomials and systems of linear equations, the constants c and d of the expression p(x) = x⁴ - 5 · x³ - 7 · x² + c · x + d are 29 and 30.
To learn more on polynomials: brainly.com/question/11536910
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F(x) = 2^x
(The ‘^’ means ‘to the power of’)
To find this function, you first need to notice that the y values are powers of 2, and you can tell because they are doubling each time x increases: 4 × 2 = 8, 8 × 2 = 16, etc.
Once you’ve noticed that they are powers of 2, you then need to find out which powers of 2 they are. The first y value is 4 which equals 2², and the second y value is 8 which equals 2³.
This means that the power is the x value, so you end up with f(x) = 2^x
I hope this helps!
