Question

1. x² - х - 6 = 0 2. 2х² - 4х - 30 = 0 3. х² + 15х - 100 = 0

Answer 1

1.
d=1*1+4*6=1+24=25
√25=5
x1=(1+5/2)=6/2=3
x2=(1-5/2)=-4/2=-2
2.
d=4*4+4*2*30=16+240=256
√256=16
x1=(4+16/4)=20/4=5
x2=(4-16/4)=-12/4=-3
3.
d=15*15+4*100=225+400=625
√625=25
x1=(-15+25/2)=10/2=5
x2=(-15-25/2)=-40/2=-20

Answer 2

1.D=b^2-4ac
D=1-4•1•(-6)=25, √D=5
x1=-b+√D/2a= 1+5/2= 3
x2=-b-√D/2a=1-5/2= -2
2.D=b^2-4ac
D=16-4•2•(-30)=256, √D=16
x1=-b+√D/2a=4+16/4=5
x2=-b-√D/2a=4-16/4=-3
3. .D=b^2-4ac
D=225-4•1•(-100)=625, √D=25
x1=-b+√D/2a= -15+25/2=5
x2=-b-√D/2a=-15-25/2=-20

Answer 3

To solve these quadratic equations, we can use the quadratic formula, which is given by:

For a quadratic equation of the form ax² + bx + c = 0, the solutions for x are given by:

x = (-b ± √(b² - 4ac)) / 2a

Let's solve each of the given equations using the quadratic formula:

1. x² - х - 6 = 0: Here, a = 1, b = -1, and c = -6. Plugging these values into the quadratic formula:

x = (1 ± √((-1)² - 4 * 1 * (-6))) / 2 * 1 x = (1 ± √(1 + 24)) / 2 x = (1 ± √25) / 2

Now, we have two possible solutions for x:

x₁ = (1 + √25) / 2 = (1 + 5) / 2 = 6 / 2 = 3 x₂ = (1 - √25) / 2 = (1 - 5) / 2 = -4 / 2 = -2

So the solutions for the equation x² - х - 6 = 0 are x = 3 and x = -2.

2. 2х² - 4х - 30 = 0: Here, a = 2, b = -4, and c = -30. Plugging these values into the quadratic formula:

x = (-(-4) ± √((-4)² - 4 * 2 * (-30))) / 2 * 2 x = (4 ± √(16 + 240)) / 4 x = (4 ± √256) / 4 x = (4 ± 16) / 4

Now, we have two possible solutions for x:

x₁ = (4 + 16) / 4 = 20 / 4 = 5 x₂ = (4 - 16) / 4 = -12 / 4 = -3

So the solutions for the equation 2х² - 4х - 30 = 0 are x = 5 and x = -3.

3. х² + 15х - 100 = 0: Here, a = 1, b = 15, and c = -100. Plugging these values into the quadratic formula:

x = (-15 ± √(15² - 4 * 1 * (-100))) / 2 * 1 x = (-15 ± √(225 + 400)) / 2 x = (-15 ± √625) / 2 x = (-15 ± 25) / 2

Now, we have two possible solutions for x:

x₁ = (-15 + 25) / 2 = 10 / 2 = 5 x₂ = (-15 - 25) / 2 = -40 / 2 = -20

So the solutions for the equation х² + 15х - 100 = 0 are x = 5 and x = -20.