Quadratic funtion and geometric calculus help? (1 Viewer)

[renny 123]

Q1. Let a and b be the roots of 3x^2+4x-7=0 Without solving, find the value of a^3+b^3

Q2. The curve has the second derivative = 8x and the tangent at (-2, 5) makes an angle of 45 degrees with the x-axis. Find the equation of the curve.

Thanks to anyone who can help

 

[Iruka]

For q1, using sum and product of roots you can find a+b and ab.

(a+b)^3 = a^3+3a^2b+3ab^2 +b^3
= a^3+b^3 +3ab(a+b)

I think you can work it out from there.

 

[bored of sc]

Q1. Let a and b be the roots of 3x^2+4x-7=0 Without solving, find the value of a^3+b^3

Q2. The curve has the second derivative = 8x and the tangent at (-2, 5) makes an angle of 45 degrees with the x-axis. Find the equation of the curve.

Thanks to anyone who can help

1. a³+b³ = (a+b)(a²-ab+b²)

Now a²+b² = (a+b)²-2ab

Thus a³+b³ = (a+b)[(a+b)²-3ab]

a+b = -b/a = -4/3
ab = c/a = -7/3

a³+b³ = (-4/3)[(-4/3)²-2(-7/3)]
= -4/3(-16/9+14/3)
= -4/3(-16/9+42/9)
= -4/3(26/9)
= -104/27

If my non-calculator skills are up to scratch.


2. f''(x) = 8x
f'(x) = 4x²+C
f'(-2) = 4(-2)² +C = tan45 = 1

C = 1-16
= -15
f'(x) = 4x²-15

f(x) = 4x³/3 -15x +C
f(-2) = 4(-2)³/3 -15(-2) +C = 5

C = 5+32/3-30
= -43/3

f(x) = 4x³/3 -15x -43/3


Excuse any silly errors. Sorry if there are any.