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Gennadij [26K]
3 years ago
10

1) 3r² – 2r=-9 Quadratic formula

Mathematics
1 answer:
Nonamiya [84]3 years ago
3 0

Answer:

Solving the equation 3r^2-2r=-9 using quadratic formula we get: \mathbf{ r=\frac{1+\sqrt{26}\:i}{3}\:or\: r=\frac{1-\sqrt{26}\:i}{3}}

Step-by-step explanation:

We need to solve the equation 3r^2-2r=-9 using quadratic formula.

The quadratic formula is: r=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

For the given equation: 3r^2-2r=-9

We can write it as: 3r^2-2r+9=0

We have a = 3, b= -2 and c=9

Putting values in quadratic formula and finding value of r

r=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\r=\frac{-(-2)\pm\sqrt{(-2)^2-4(3)(9)}}{2(3)}\\r=\frac{2\pm\sqrt{4-108}}{6}\\r=\frac{2\pm\sqrt{-104}}{6}\\We\:know\:that: \sqrt{-1}=i\\ r=\frac{2\pm\sqrt{26} \:i}{6}\\ r=\frac{2+2\sqrt{26}\:i}{6}\:or\: r=\frac{2-2\sqrt{26}\:i}{6}\\ r=\frac{2(1+\sqrt{26}\:i)}{6}\:or\: r=\frac{2(1-\sqrt{26}\:i)}{6}\\ r=\frac{1+\sqrt{26}\:i}{3}\:or\: r=\frac{1-\sqrt{26}\:i}{3}

So, solving the equation 3r^2-2r=-9 using quadratic formula we get: \mathbf{ r=\frac{1+\sqrt{26}\:i}{3}\:or\: r=\frac{1-\sqrt{26}\:i}{3}}

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