Solve the following quadratic equation whose roots are.

1)5 and - 9
2)-1 and - 1/2
3)4 and - 11
4)1 and 1 whole number 1/2

simplest way:

#1, if the roots are 5 and -9, then we have
(x-5)(x+9) = 0
expand this and simplify
x^2 + 4x - 45 = 0

do the others the same way

1)5 and - 9

That means
(x-5)(x+9) = 0
x^2 + 4 x - 45 - 0
if roots are a and b
equation was
(x-a)(x-b) = 0

eg for #4 if you mean 1.5
( x-1) (x- 3/2) = 0
multiply both sides by 2
(x-1)(2x-3) = 0
2 x^2 -5 x + 3 = 0

To solve the quadratic equations, we can use the fact that the sum and the product of the roots of a quadratic equation are related to the coefficients of the equation.

1) The quadratic equation with roots 5 and -9 can be written as (x-5)(x+9) = 0.

Expanding this equation, we get x^2 + 9x - 5x - 45 = 0.

Combining like terms, we have x^2 + 4x - 45 = 0.

Therefore, the quadratic equation with roots 5 and -9 is x^2 + 4x - 45 = 0.

2) The quadratic equation with roots -1 and -1/2 can be written as (x+1)(x+1/2) = 0.

Expanding this equation, we get x^2 + (1/2)x + x + (1/2)*1/2 = 0.

Combining like terms, we have x^2 + (3/2)x + 1/4 = 0.

Therefore, the quadratic equation with roots -1 and -1/2 is x^2 + (3/2)x + 1/4 = 0.

3) The quadratic equation with roots 4 and -11 can be written as (x-4)(x+11) = 0.

Expanding this equation, we get x^2 + 11x - 4x - 44 = 0.

Combining like terms, we have x^2 + 7x - 44 = 0.

Therefore, the quadratic equation with roots 4 and -11 is x^2 + 7x - 44 = 0.

4) The quadratic equation with roots 1 and 1/2 can be written as (x-1)(x-1/2) = 0.

Expanding this equation, we get x^2 - (1/2)x - x + (1/2)*(1/2) = 0.

Combining like terms, we have x^2 - (3/2)x + 1/4 = 0.

Therefore, the quadratic equation with roots 1 and 1/2 is x^2 - (3/2)x + 1/4 = 0.

Note: In all of the above equations, the coefficients may vary depending on any constant multiplier.

To solve a quadratic equation, we can use the quadratic formula, which is given by:

x = (-b ± √(b^2 - 4ac)) / 2a

where "a," "b," and "c" are the coefficients of the quadratic equation in the standard form ax^2 + bx + c = 0.

1) Roots: 5 and -9
The quadratic equation with roots 5 and -9 can be written as:
(x - 5)(x + 9) = 0

Expanding this equation, we get:
x^2 - 5x + 9x - 45 = 0
x^2 + 4x - 45 = 0

Comparing this equation with ax^2 + bx + c = 0, we have:
a = 1, b = 4, c = -45

Using the quadratic formula:
x = (-4 ± √(4^2 - 4(1)(-45))) / (2(1))
x = (-4 ± √(16 + 180)) / 2
x = (-4 ± √196) / 2
x = (-4 ± 14) / 2

Simplifying further, we get:
x1 = (-4 + 14) / 2 = 10 / 2 = 5
x2 = (-4 - 14) / 2 = -18 / 2 = -9

Therefore, the roots of the quadratic equation are 5 and -9.

2) Roots: -1 and -1/2
The quadratic equation with roots -1 and -1/2 can be written as:
(x + 1)(x + 1/2) = 0

Expanding this equation, we get:
x^2 + 1/2x + x + 1/2 = 0
x^2 + (3/2)x + 1/2 = 0

Comparing this equation with ax^2 + bx + c = 0, we have:
a = 1, b = 3/2, c = 1/2

Using the quadratic formula:
x = (-(3/2) ± √((3/2)^2 - 4(1)(1/2))) / (2(1))
x = (-3/2 ± √(9/4 - 2/2)) / 2
x = (-3/2 ± √(9/4 - 1)) / 2
x = (-3/2 ± √(9/4 - 4/4)) / 2
x = (-3/2 ± √(5/4)) / 2
x = (-3/2 ± (√5)/2) / 2

Simplifying further, we get:
x1 = (-3/2 + √5/2) / 2 = (-3 + √5) / 4
x2 = (-3/2 - √5/2) / 2 = (-3 - √5) / 4

Therefore, the roots of the quadratic equation are (-3 + √5)/4 and (-3 - √5)/4.

3) Roots: 4 and -11
The quadratic equation with roots 4 and -11 can be written as:
(x - 4)(x + 11) = 0

Expanding this equation, we get:
x^2 + 11x - 4x - 44 = 0
x^2 + 7x - 44 = 0

Comparing this equation with ax^2 + bx + c = 0, we have:
a = 1, b = 7, c = -44

Using the quadratic formula:
x = (-7 ± √(7^2 - 4(1)(-44))) / (2(1))
x = (-7 ± √(49 + 176)) / 2
x = (-7 ± √225) / 2
x = (-7 ± 15) / 2

Simplifying further, we get:
x1 = (-7 + 15) / 2 = 8 / 2 = 4
x2 = (-7 - 15) / 2 = -22 / 2 = -11

Therefore, the roots of the quadratic equation are 4 and -11.

4) Roots: 1 and 1/2
The quadratic equation with roots 1 and 1/2 can be written as:
(x - 1)(x - 1/2) = 0

Expanding this equation, we get:
x^2 - x - 1/2x + 1/2 = 0
x^2 - (3/2)x + 1/2 = 0

Comparing this equation with ax^2 + bx + c = 0, we have:
a = 1, b = -3/2, c = 1/2

Using the quadratic formula:
x = (-(3/2) ± √((-3/2)^2 - 4(1)(1/2))) / (2(1))
x = (-3/2 ± √(9/4 - 2/2)) / 2
x = (-3/2 ± √(9/4 - 1)) / 2
x = (-3/2 ± √(9/4 - 4/4)) / 2
x = (-3/2 ± √(5/4)) / 2
x = (-3/2 ± (√5)/2) / 2

Simplifying further, we get:
x1 = (-3/2 + √5/2) / 2 = (-3 + √5) / 4
x2 = (-3/2 - √5/2) / 2 = (-3 - √5) / 4

Therefore, the roots of the quadratic equation are (-3 + √5)/4 and (-3 - √5)/4.