Question

1) 3r² – 2r=-9 Quadratic formula

Answer 1

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: $\mathbf{ r=\frac{1+\sqrt{26}\:i}{3}\:or\: r=\frac{1-\sqrt{26}\:i}{3}}$