Polynomial Equations & Inequalities

[harry_gary12]

Polynomial Equations & Inequalities [Solved]

Hi,

I've no idea at all how to solve this question. If you could guide me, I would really appreciate it.

A stunt pilot is testing a new plane. The equation that models his height over time is f(x)=15x^2-195x+950, where x is his time in second and f(x) is his height in metres. determine when the pilot is below 500 metres.

Thank you

I've from my solution. Credits to John T from yahoo answers.

"15^x2 - 195x +950 < 500

15x^2 - 195x +450 < 0

3x^2 - 39x + 90 < 0
x^2 - 13x + 30 < 0

(x-10)(x-3) < 0

He's below 500 meters between 3 and 10 seconds of his flight."

or 3<x<10

 

[harry_gary12]

Do you still have a question?

Nope. Thanks anyway!

 

[HallsofIvy]

Hi,

I've no idea at all how to solve this question. If you could guide me, I would really appreciate it.

A stunt pilot is testing a new plane. The equation that models his height over time is f(x)=15x^2-195x+950, where x is his time in second and f(x) is his height in metres. determine when the pilot is below 500 metres.

Thank you

I've from my solution. Credits to John T from yahoo answers.

"15^x2 - 195x +950 < 500

15x^2 - 195x +450 < 0

3x^2 - 39x + 90 < 0
x^2 - 13x + 30 < 0

Do you see that you have divided the inequality by 5 and then 3 (and could have divided the original inequality by 15) and why it is important that those numbers are positive?

(x-10)(x-3) < 0

He's below 500 meters between 3 and 10 seconds of his flight."

or 3<x<10

If a product of numbers is negative, then the numbers must be of opposite sign. So either x- 10> 0 and x- 3< 0 or
x- 10< 0 and x- 3> 0. If x- 10> 0 then x> 10 so x- 3> 7. x- 3< 0 is impossible. If x- 10< 0 then x< 10 and x- 3> 0 gives x> 3: 3< x< 10. Yes, x must be between 3 and 10.