polynomial division

**stormerze** · November 13th 2008, 12:52 AM

I can't figure out these 2 questions from the applications section.

P(x) = $x^3 - 2x^2 - ax + b$ and x-3 is a factor of P(x)
Q (x) = $ax^2 + bx - 5$ and Q(-2) = -2

Find the values of a and b

Second Question:

A tennis ball thrown into the air follows a curved path described by the equation $h= -2t^2 + 5t + 2$
H is height, t is seconds

What was the greatest height the ball reached during its flight.

Looking for explanations rather than answers.

Thanks.

**mr fantastic** · November 13th 2008, 12:57 AM

Originally Posted by stormerze

I can't figure out these 2 questions from the applications section.

P(x) = $x^3 - 2x^2 - ax + b$ and x-3 is a factor of P(x)
Q (x) = $ax^2 + bx - 5$ and Q(-2) = -2

Find the values of a and b

Mr F says: If x - 3 is a factor of P(x) then P(3) = 0. Therefore:

${\color{red}0 = 3^3 - 2(3)^2 - 3a + b \Rightarrow 0 = 9 - 3a + b}$ .... (1)

Q(-2) = -2 therefore:

${\color{red}-2 = a(-2)^2 + b(-2) - 5 \Rightarrow 2 = 4a - 2b}$ .... (2)

Solve equations (1) and (2) simultaneously.

[snip]

..

**mr fantastic** · November 13th 2008, 01:02 AM

Originally Posted by stormerze

[snip]
Second Question:

A tennis ball thrown into the air follows a curved path described by the equation $h= -2t^2 + 5t + 2$
H is height, t is seconds

What was the greatest height the ball reached during its flight.

Looking for explanations rather than answers.

Thanks.

Complete the square:

$h = -2 \left(t - \frac{5}{4}\right)^2 + \frac{41}{8}$ .

Read off the turning point. The h-coordinate of the turning point gives the maximum height. I'm renowned for making careles mistakes so you should confirm the above equation - carefully.

**stormerze** · November 13th 2008, 01:07 AM

Thanks, i'll try it and get back to you

Also can you explain this question.
$<br /> 3x^2 - 4x - 9 = 0$ - Calculate the value of the discriminant and state the nature of the solutions (rational or irrational)

**stormerze** · November 13th 2008, 01:20 AM

I managed to get the answer but I have a few questions.

Why do we use the x intercept and not the last bit of what you posted 41/8

Is it 41/8 or 41/16, I for some reason get - 41/16

**mr fantastic** · November 13th 2008, 04:01 AM

Originally Posted by stormerze

I managed to get the answer but I have a few questions.

Why do we use the x intercept and not the last bit of what you posted 41/8

Is it 41/8 or 41/16, I for some reason get - 41/16

Are you familiar with the turning point form of a parabola and what it tells you?

$y = a(x - h)^2 + k$ has a turning point at x = h and y = k.

This is one of several ways of getting a turning point. I'm assuming you've been taught some of them ....?

**mr fantastic** · November 13th 2008, 04:02 AM

Originally Posted by stormerze

Thanks, i'll try it and get back to you

Also can you explain this question.
$<br /> 3x^2 - 4x - 9 = 0$ - Calculate the value of the discriminant and state the nature of the solutions (rational or irrational)

Please state the formula for the discriminant. Then state for me the value of a, b and c for this particular quadratic equation.

Now .... where exactly are you stuck?

By the way - new unrelated questions should be posted as a new thread.

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