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3 years ago

Let $r$ and $s$ be the roots of $3x^2 + 4x + 12 = 0.$ Find $r^2 + s^2.$ Pls help.

Mathematics

1 answer:

nirvana33 [79]3 years ago

5 0

Answer:

-56/9

Step-by-step explanation:

By Vieta's formulas,

$r + s = -\frac{4}{3}$ and $rs = \frac{12}{3} = 4.$ Squaring the equation $r + s = -\frac{4}{3},$ we get

$r^2 + 2rs + s^2 = \frac{16}{9}.$ Therefore,

$r^2 + s^2 = \frac{16}{9} - 2rs = \frac{16}{9} - 2 \cdot 4 = -\frac{56}{9}}$

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natka813 [3]

Answer:

The coordinates of the science lab is:

x = -14/3 , y = 1

Step-by-step explanation:

∵ P is (-8 , -1) and Q is (2 , 5)

∵ The point of the science lab is (x , y)

∵ The science lab point divided PQ at ratio 2 : 1 from Q (two thirds PQ)

∴ $x=\frac{m_{1}x_{p}+m_{2}x_{q}}{m_{1}+m_{2}}$

∴ $y=\frac{m_{1}y_{p}+m_{2}y_{q}}{m_{1}+m_{2}}$

∴ $x=\frac{2(-8)+1(2)}{1+2}=\frac{-14}{3}$

∴ $y=\frac{2(-1)+1(5)}{2+1}=\frac{3}{3}=1$

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