1. Which statement best describes the polynomial 2x^3-4?

Mathematics

1 answer:

anastassius [24]2 years ago

5 0

X cube means it is a third degree function. 2x cube is 1 term and -4 is another. so B.

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How do i check an equation for extraneous solutions?

Marina86 [1]

Example:

$\sqrt x(x+1)=0$

This suggests two solutions, $x=0$ and $x=-1$ .

However, upon plugging these solutions back into the equation, you get

$\sqrt0(0+1)=0(1)=0$

which checks out, but

$\sqrt{-1}(1-1)=0$

does not because $\sqrt x$ is defined only for $x\ge0$ (assuming you're looking for real solutions only). So, we call $x=-1$ an extraneous solution, and the complete solution set (over the real numbers) is $x=0$ .

7 0

2 years ago

Read 2 more answers

55. (a) If alpha and beta are the roots of the equation xsquare+ px+q=0 and beta>alpha find the square of the

densk [106]

Answer:

√(p²-4q)

Step-by-step explanation:

Using the Quadratic Formula, we can say that

x = ( -p ± √(p²-4(1)(q))) / 2(1) with the 1 representing the coefficient of x². Simplifying, we get

x = ( -p ± √(p²-4q)) / 2

The roots of the function are therefore at

x = ( -p + √(p²-4q)) / 2 and x = ( -p - √(p²-4q)) / 2. The difference of the roots is thus

( -p + √(p²-4q)) / 2 - ( ( -p - √(p²-4q)) / 2)

= 0 + 2 √(p²-4q)/2

= √(p²-4q)

7 0

2 years ago

What is the solution set of x2 + 5x + 1 = 0?

DerKrebs [107]

Answer:

$\huge\boxed{\left\{-\dfrac{5+\sqrt{21}}{2};\ \dfrac{-5+\sqrt{21}}{2}\right\}}$

Step-by-step explanation:

$x^2+5x+1=0\\\\\text{Use the quadratic formula:}\\\\\text{For}\ ax^2+bx+c=0\\\\\Delta=b^2-4ac\\\\\text{if}\ \Delta < 0,\ \text{then the equation has no real solution}\\\text{if}\ \Delta=0,\ \text{then the equation has one real solution}\ x=\dfrac{-b}{2a}\\\text{if}\ \Delta>0,\ \text{then the equation has two real solution}\ x=\dfrac{-b\pm\sqrt{\Delta}}{2a}$