QuestionSolve the inequality $y^{2}+y-2 \leq 0$ .

Studdy Solution

STEP 1

Assumptions1. We are solving the inequality $y^{}+y- \leq0$ .

STEP 2

First, we need to factor the quadratic equation. We are looking for two numbers that multiply to -2 and add to1.
$y^{2}+y-2 = (y-1)(y+2)$

STEP 3

Now, we set each factor equal to zero and solve for y.
$y-1 =0 \Rightarrow y =1$ $y+2 =0 \Rightarrow y = -2$

STEP 4

We have found the roots of the equation, which are y =1 and y = -2. These are the points where the quadratic equation crosses the y-axis.

STEP 5

The quadratic equation will be less than or equal to zero between these two roots. We can check this by testing a value between -2 and1. Let's use0 as a test value.
$0^{2}+0-2 = -2$

STEP 6

Since -2 is less than0, we can conclude that the quadratic equation is less than or equal to zero between the roots y = -2 and y =1.

STEP 7

Therefore, the solution to the inequality $y^{2}+y-2 \leq0$ is $-2 \leq y \leq1$ .
The solution is $-2 \leq y \leq1$ .

Was this helpful?

QuestionSolve the inequality $y^{2}+y-2 \leq 0$ .

Studdy Solution

STEP 1

Assumptions1. We are solving the inequality $y^{}+y- \leq0$ .

STEP 2

First, we need to factor the quadratic equation. We are looking for two numbers that multiply to -2 and add to1.
$y^{2}+y-2 = (y-1)(y+2)$

STEP 3

Now, we set each factor equal to zero and solve for y.
$y-1 =0 \Rightarrow y =1$ $y+2 =0 \Rightarrow y = -2$

STEP 4

We have found the roots of the equation, which are y =1 and y = -2. These are the points where the quadratic equation crosses the y-axis.

STEP 5

The quadratic equation will be less than or equal to zero between these two roots. We can check this by testing a value between -2 and1. Let's use0 as a test value.
$0^{2}+0-2 = -2$

STEP 6

Since -2 is less than0, we can conclude that the quadratic equation is less than or equal to zero between the roots y = -2 and y =1.

STEP 7

Therefore, the solution to the inequality $y^{2}+y-2 \leq0$ is $-2 \leq y \leq1$ .
The solution is $-2 \leq y \leq1$ .

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionSolve the inequality y2+y−2≤0y^{2}+y-2 \leq 0y2+y−2≤0.

Studdy Solution

STEP 1

Assumptions1. We are solving the inequality y+y−≤0y^{}+y- \leq0y+y−≤0.

STEP 2

First, we need to factor the quadratic equation. We are looking for two numbers that multiply to -2 and add to1.y2+y−2=(y−1)(y+2)y^{2}+y-2 = (y-1)(y+2)y2+y−2=(y−1)(y+2)

STEP 3

Now, we set each factor equal to zero and solve for y.y−1=0⇒y=1y-1 =0 \Rightarrow y =1y−1=0⇒y=1y+2=0⇒y=−2y+2 =0 \Rightarrow y = -2y+2=0⇒y=−2

STEP 4

We have found the roots of the equation, which are y =1 and y = -2. These are the points where the quadratic equation crosses the y-axis.

STEP 5

The quadratic equation will be less than or equal to zero between these two roots. We can check this by testing a value between -2 and1. Let's use0 as a test value.02+0−2=−20^{2}+0-2 = -202+0−2=−2

STEP 6

Since -2 is less than0, we can conclude that the quadratic equation is less than or equal to zero between the roots y = -2 and y =1.

STEP 7

Therefore, the solution to the inequality y2+y−2≤0y^{2}+y-2 \leq0y2+y−2≤0 is −2≤y≤1-2 \leq y \leq1−2≤y≤1.The solution is −2≤y≤1-2 \leq y \leq1−2≤y≤1.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionSolve the inequality $y^{2}+y-2 \leq 0$ .

Assumptions1. We are solving the inequality $y^{}+y- \leq0$ .

First, we need to factor the quadratic equation. We are looking for two numbers that multiply to -2 and add to1.
$y^{2}+y-2 = (y-1)(y+2)$

Now, we set each factor equal to zero and solve for y.
$y-1 =0 \Rightarrow y =1$ $y+2 =0 \Rightarrow y = -2$

The quadratic equation will be less than or equal to zero between these two roots. We can check this by testing a value between -2 and1. Let's use0 as a test value.
$0^{2}+0-2 = -2$

Therefore, the solution to the inequality $y^{2}+y-2 \leq0$ is $-2 \leq y \leq1$ .
The solution is $-2 \leq y \leq1$ .