Solve for x 0>x^2+5x-2

Problem

0>x2+5*x−2

Solution

1. Rewrite the inequality in standard form to find the roots of the quadratic expression.

x2+5*x−2<0

2. Identify the coefficients of the quadratic equation a*x2+b*x+c=0

a=1

b=5

c=−2

3. Apply the quadratic formula to find the critical points where the expression equals zero.

x=(−b±√(,b2−4*a*c))/(2*a)

x=(−5±√(,5−4*(1)*(−2)))/(2*(1))

x=(−5±√(,25+8))/2

x=(−5±√(,33))/2

4. Determine the intervals based on the roots. The roots are (x_1)=(−5−√(,33))/2 and (x_2)=(−5+√(,33))/2

(−5−√(,33))/2≈−5.37

(−5+√(,33))/2≈0.37

5. Analyze the parabola y=x2+5*x−2 Since the leading coefficient a=1 is positive, the parabola opens upward. The expression is less than zero between the two roots.

(−5−√(,33))/2<x<(−5+√(,33))/2

Final Answer

x∈((−5−√(,33))/2,(−5+√(,33))/2)

Want more problems? Check here!