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Sagot :
To find the roots of a polynomial of degree 3 we can use quadratic formula.
To find the roots of a polynomial function, also known as its zeros, you can use several methods. One method is to use the quadratic formula, which is a general formula that can be used to find the roots of a polynomial of degree 2 (quadratic).
If the polynomial is of degree 3 (cubic), you can use the cubic formula, which is a bit more complicated than the quadratic formula. The cubic formula is:
x = (-b + sqrt(b^2 - 4ac))/(2a) , (-b - sqrt(b^2 - 4ac))/(2a)
where a, b, and c are the coefficients of the polynomial in the form:
ax^3 + bx^2 + cx + d = 0
For example, if you have the polynomial x^3 - 7x^2 + 15x - 9 = 0, then a=1, b=-7, c=15, and d=-9. Plugging these values into the cubic formula gives you:
x = (-(-7) + sqrt((-7)^2 - 4115))/(21) , (-(-7) - sqrt((-7)^2 - 4115))/(21)
which simplifies to:
x = (7 + sqrt(49 - 60))/2 , (7 - sqrt(49 - 60))/2
This gives you two solutions: x = 2 and x = -3.
If you don't want to use the cubic formula, you can also try factoring the polynomial into linear factors. For example, the polynomial x^3 - 7x^2 + 15x - 9 can be factored as (x-1)(x-3)(x-3) = 0, which gives you the roots x=1, x=3, and x=3.
You can also use a graphing calculator or computer software to find the roots of a polynomial. Many of these tools will also give you the option to see the steps involved in finding the roots, which can be helpful for understanding the process.
Learn more about quadratic formula, here https://brainly.com/question/9300679
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