putaprincess16

19.02.2021 •

Mathematics

∠DAC=∠BAD
What is the length of AB?
Round to one decimal place.

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Ответ:

natalie407888

19.03.2020

Mathematics

The correct option is $\boxed{\bf option (c)}$ i.e., $\boxed{D=0}$ .

Further explanation:

Given that x=-3 is the only -intercept of the graph of a quadratic equation.

The -intercepts is the location where the output of the function is zero that is f(x)=0 .

The number of -intercept depends upon the location of the graph.

The discriminant of the quadratic equation $ax^{2}+bx+c=0$ is calculated as follows:

$\boxed{D=b^{2}-4ac}$

If then there are two real roots, if D=0 then there are only one real root and if then there will be no real root.

If the discriminant is less than , then the parabola of the quadratic function does not intersect the -axis.

If the discriminant is equal to zero then the parabola will touch the -axis at only one point.

If the discriminant is greater than zero then the parabola will intersect the -axis at two points.

Since, is equal to is the only intercept therefore, the equation is,

$\begin{aligned}\left({x-\left({-3}\right)}\right)\left({x-\left({-3}\right)}\right)&=0\\\left({x+3}\right)\left({x+3}\right)&=0\\{x^2}+2\cdot 3x+{3^2}&=0\\{x^2}+6x+9&=0{\text{}}......{\text{ (1)}} \\ \end{aligned}$

In the above equation $a=1,b=6\text{ and }c=9$ .

The discriminant of equation (1) is calculated as follows:

$\begin{aligned}D&={b^2} - 4ac \\&={6^2}-4\times 1\times 9\\&=36-36\\&=0\\\end{aligned}$

Therefore, the discriminant is equal to .

Thus, the correct option is $\boxed{\bf option (c)}$ .

Learn more:

1. A problem on composite function

2. A problem to find radius and center of circle

3. A problem to determine intercepts of a line

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Quadratic equation

Keywords: x-intercept, quadratic function, quadratic equation x= - 3, parabola, discriminant, D>0, D<0, D=0, roots, real roots, equal roots, imaginary roots, curve.

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∠DAC=∠BAD What is the length of AB? Round to one decimal place.