Problem

Solve the quadratic inequality x2−3x−4>0

Answer

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Answer

Therefore, the solution set for x2−3x−4>0 is x<−1 or x>4

Steps

Step 1 ：First, we solve the corresponding equation x2−3x−4=0

Step 2 ：This can be factored into (x−4)(x+1)=0

Step 3 ：The solutions are x=4 and x=−1

Step 4 ：Now we consider the inequality x2−3x−4>0

Step 5 ：The parabola y=x2−3x−4 opens upwards, and the roots of the equation are the x-coordinates of the vertex.

Step 6 ：We know that the y-values are positive when x is less than -1 or x is greater than 4.

Step 7 ：Therefore, the solution set for x2−3x−4>0 is x<−1 or x>4

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