Question

Evan graphed a cubic function, f(x) = ax3 + bx2 + cx + d, and determined the roots of f(x) to be +1 and 2. What is the value of b, if a = 1

Answer 1

The value of $b$ in the cubic polynomial is -4.

How to determine the coefficients of a cubic polynomial

After a quick analysis, we find that given cubic function is equivalent to the following equivalence:

$x^{3}+b\cdot x^{2}+c\cdot x + d = (x-1)^{2}\cdot (x-2)$

$x^{3}+b\cdot x^{2}+c\cdot x + d = (x^{2}-2\cdot x + 1)\cdot (x-2)$

$x^{3}+b\cdot x^{2}+c\cdot x + d = x^{3}-2\cdot x^{2}+x-2\cdot x^{2}+4\cdot x-2$

$x^{3}+b\cdot x^{2}+c\cdot x + d = x^{3}-4\cdot x^{2}+5\cdot x -2$

After a quick observation, we conclude that the value of $b$ in the cubic polynomial is -4. $\blacksquare$

To learn more on polynomials, we kindly invite to check this verified question: brainly.com/question/17822016