If the equation 2x(x - 1) = 3 - x is solved for x, what is the larger of the two solutions… — ACT

If the equation $2x(x - 1) = 3 - x$ is solved for $x$ , what is the larger of the two solutions?

Cevap: 1.5

The larger of the two solutions is

1.5

Expanding the equation

2x(x - 1) = 3 - x

results in

2x^2 - 2x = 3 - x

. Setting this quadratic equation to zero yields

2x^2 - x - 3 = 0

. Factoring the expression gives

(2x - 3)(x + 1) = 0

. Setting the first factor to zero,

2x - 3 = 0

, results in

x = 1.5

. Setting the second factor to zero,

x + 1 = 0

, results in

x = -1

. Comparing the two values,

1.5

is the larger solution.

Expand and rearrange the equation into standard quadratic form

ax^2 + bx + c = 0

2x^2 - x - 3 = 0

A quadratic equation must be set to zero before solving it by factoring.

Factor the quadratic trinomial by grouping.

(2x - 3)(x + 1) = 0

Factoring allows us to apply the zero product property.

Set each factor to zero to solve for the roots.

x = 1.5

and

x = -1

If a product equals zero, at least one of its factors must be zero.

Compare the solutions to find the larger value.

1.5

Comparing

1.5

and

-1

shows that

1.5

is the greater value.

Solving quadratic equations by factoring when the leading coefficient is greater than 1

Soru