Question

3x^2-4x-5=0 y^2-8y+12

Answer 1

1) 3x²-4x-5=0
 D=(-4)²-4*(-5)*3=76
$x_{1}= \frac{4- \sqrt{76} }{6}= \frac{2- \sqrt{19} }{3}$
$x_{2}= \frac{4+ \sqrt{76} }{6}= \frac{2+ \sqrt{19} }{3}$

2) y²-8y+12=0
D=(-8)²-4*12=64-48=16
y1=2; y2=6

Answer 2

Y^2-8y+12=0
D=64-4*12=64-48=16=4^2
x1.2= (8 +- 4)/2
x1=6
x2=2

Answer 3

It looks like you've given two equations, one quadratic equation and one quadratic expression. To solve the quadratic equation and simplify the quadratic expression, I'll start with the quadratic equation:

1. Quadratic Equation: 3x^2 - 4x - 5 = 0

To solve this equation, you can use the quadratic formula, which is given by:

x = (-b ± √(b² - 4ac)) / (2a)

In this equation, a = 3, b = -4, and c = -5. Plugging these values into the formula:

x = (-(-4) ± √((-4)² - 4(3)(-5))) / (2(3)) x = (4 ± √(16 + 60)) / 6 x = (4 ± √76) / 6

You can simplify this expression further if needed:

x = (4 ± 2√19) / 6

Now, let's move on to the quadratic expression:

2. Quadratic Expression: y^2 - 8y + 12

This expression can be factored:

y^2 - 8y + 12 = (y - 6)(y - 2)

So, the simplified form of the expression is:

y^2 - 8y + 12 = (y - 6)(y - 2)

These are the solutions to your equations and the simplified form of the quadratic expression. If you need any further assistance or have specific questions, please let me know.