Quadratic Functions (1 Viewer)

[kbei]

hey guys, thanks for reading, just couldnt figure these questions out:

If a and b are the roots of the equation px^2 + qx + r = 0 find, in terms of p,q and r

a)1/a^2 + 1/b^2
b) a^b+ab^2

When it says in terms of p,q and r, does every equation have to have all three terms?

Cheers

 

[gurmies]

a) px² + qx + r = 0

a + b = -q/p

ab = r/p

1/a² + 1/b² = (b² + a²)/(a²b²)

= (b² + a²)/(ab)²

Now, (a+b)² = a² + b² + 2ab

So a² + b² = (a+b)² - 2ab

[(a+b)² - 2ab]/(ab)²

= (q²/p² - 2r/p)/(r²/p²)

= (q² - 2rp)/r²

b) Not too sure about this one...unless you mean a²b+ab² in which case solution would be:

ab(a + b) = (r/p)(-q/p) = -qr/p²

 

[kaz1]

hey guys, thanks for reading, just couldnt figure these questions out:

If a and b are the roots of the equation px^2 + qx + r = 0 find, in terms of p,q and r

a)1/a^2 + 1/b^2
b) a^b+ab^2

When it says in terms of p,q and r, does every equation have to have all three terms?

Cheers

b) a²+b²
(a+b)²-2ab
(-q/p)² -2(r/p)
q²/p² -2r/p
(q²-2rp)/p²