The function y=ax²+bx+c: Identifying and defining elements

The quadratic equation of the given problem is already arranged (that is, all the terms are found on one side and the 0 on the other side), thus we approach the given problem as follows;

In the problem, the question was asked: what is the value of the coefficient$b$in the equation?

Let's remember the definitions of coefficients when solving a quadratic equation as well as the formula for the roots:

The rule says that the roots of an equation of the form

$ax^2+bx+c=0$are :

$x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

That is the coefficient$b$is the coefficient of the term in the first power -$x$We then examine the equation of the given problem:

$$$3x^2+8x-5 =0$That is, the number that multiplies

$x$ is

$8$Consequently we are able to identify b, which is the coefficient of the term in the first power, as the number$8$,

Thus the correct answer is option d.

The quadratic equation of the given problem has already been arranged (that is, all the terms are on one side and 0 is on the other side) thus we can approach the question as follows:

In the problem, the question was asked: what is the value of the coefficient$c$in the equation?

Let's remember the definition of a coefficient when solving a quadratic equation as well as the formula for the roots:

The rule says that the roots of an equation of the form

$ax^2+bx+c=0$are:

$x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

That is the coefficient
$c$is the free term - and as such the coefficient of the term is raised to the power of zero -$x^0$(Any number other than zero raised to the power of zero equals 1:

$x^0=1$)

Next we examine the equation of the given problem:

$$$3x^2+5x=0$Note that there is no free term in the equation, that is, the numerical value of the free term is 0, in fact the equation can be written as follows:

$3x^2+5x+0=0$and therefore the value of the coefficient$c$ is 0.

Hence the correct answer is option c.