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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


Sagot :

xero099

The value of [tex]b[/tex] 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:

[tex]x^{3}+b\cdot x^{2}+c\cdot x + d = (x-1)^{2}\cdot (x-2)[/tex]

[tex]x^{3}+b\cdot x^{2}+c\cdot x + d = (x^{2}-2\cdot x + 1)\cdot (x-2)[/tex]

[tex]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[/tex]

[tex]x^{3}+b\cdot x^{2}+c\cdot x + d = x^{3}-4\cdot x^{2}+5\cdot x -2[/tex]

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

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

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