Algebraically determine the x-intercepts of this function. Please show work.

1 answer:

3 0

To determine x intercept, put y=0

x^4 - 10x^2 + 9 = 0

x^4 - 9x^2 - x^2 + 9 = 0

x^2(x^2 - 9) - 1(x^2 - 9) = 0

(x^2 - 9)(x^2-1) =0

x^2 - 9 = 0
⇒ x^2 = 9
⇒x = +3, -3

x^2 - 1 = 0
x^2 = 1
x = +1, -1

X intercepts are -3, -1, 1, 3

You might be interested in

Two feet is what percent of a yard? And please explain how I find the answer

GenaCL600 [577]

Percent means parts out of 100
x%=x/100

1 yard=3 feet
2 feet is what percent of 3 feet?
2=x% times 3
2=x/100 times 3
2=3x/100
multiply both sides by 100
200=3x
divide both sides by 3
66.6666666=x
answer is 66.66666%

4 0

2 years ago

PLEASE HELP!!! I don’t understand

asambeis [7]

Answer:

Step-by-step explanation:

Use the half angle identity for cosine:

cos(x/2)=+ or - sqrt(1+cos(x))/sqrt(2)

I'm going to figure out the sign part first for cos(x/2)...

so x is in third quadrant which puts x between 180 and 270

if we half x, x/2 this puts us between 90 and 135 (that's the second quadrant)

cosine is negative in the second quadrant

so we know that

cos(x/2)=-sqrt(1+cos(x))/sqrt(2)

Now we need cos(x)... since we are in the third quadrant cos(x) is negative...

If you draw a reference triangle sin(x)=3/5 you should see that cos(x)=4/5 ... but again cos(x)=-4/5 since we are in the third quadrant.

So let's plug it in:

cos(x/2)=-sqrt(1+4/5)/sqrt(2)

No one likes compound fractions (mini-fractions inside bigger fractions)

Multiply top and bottom inside the square roots by 5.

cos(x/2)=-sqrt(5+4)/sqrt(10)

cos(x/2)=-sqrt(9)/sqrt(10)

cos(x/2)=-3/sqrt(10)

Rationalize the denominator

cos(x/2)=-3sqrt(10)/10

3 0

2 years ago

Solve for the zeros of the quadratic function f(x) = 9x² + 6x + 1.

Nezavi [6.7K]

Answer:

$\large\boxed{x=-\dfrac{1}{3}}$

Step-by-step explanation:

$f(x)=9x^2+6x+1\\\\\text{The zeros are for}\ f(x)=0\\\\9x^2+6x+1=0\\\\9x^2+3x+3x+1=0\\\\3x(3x+1)+1(3x+1)=0\\\\(3x+1)(3x+1)=0\\\\(3x+1)^2=0\iff3x+1=0\qquad\text{subtract 1 from both sides}\\\\3x=-1\qquad\text{divide both sides by 3}\\\\x=-\dfrac{1}{3}$