128k views
3 votes
Select the values that are solutions to the inequality x2 + 3x – 4 > 0.

User Hrishikesh
by
7.7k points

2 Answers

2 votes

Answer:

So any number in the following set is a solution:


(-\infty,-4) \cup (1,\infty)

given the inequality to solve was:


x^2+3x-4>0

Explanation:

The left hand side is a quadratic while the right hand side is 0.

Since this is a quadratic>0, I'm going to factor the quadratic if possible and then solve that quadratic=0 for x.

That is I'm going to solve:


x^2+3x-4=0

Since a=1, I get to ask what multiplies to be c (-4) and add up to be b(3).

Those numbers are 4 and -1.

So the factored form for the equation is:


(x+4)(x-1)=0

Setting both factors equal to 0 since 0*anything=0:

x+4=0 and x-1=0

-4 -4 +1 +1

---------------------------------------------------

x=-4 and x=1

Ok so if this wasn't a quadratic I would make a number line and choose numbers to plug into the quadratic to see which intervals would give me positive results. I say positive due to the >0 part.

However since I know about the shapes of quadratics, I'm going to use that.

The quadratic function
f(x)=x^2+3x-4 has x-intercepts (-4,0) and (1,0) and is open up.

I determine that it was opened up because the leading coefficient is 1 which is positive.

Now the left tail and right tail is what is above the x-axis so the solution set is:


(-\infty,-4) \cup (1,\infty)

User Yoonah
by
7.8k points
7 votes

Answer:

-6 and 5

Explanation:

User Artxur
by
8.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories