Question

Solve the following polynomial inequal 5x²+27x-18<=0

Answer 1

To solve the inequality 5x²+27x-18≤0, we apply the quadratic formula to find the roots of the equation and then determine where the inequality holds by testing intervals around these roots.

Step-by-step explanation:

We are given the polynomial inequality 5x²+27x-18≤0. To solve this inequality, we use the quadratic formula to find the roots of the corresponding equation 5x²+27x-18=0. The quadratic formula for an equation of the form ax²+bx+c=0 is x = (-b ± √(b²-4ac))/(2a). Applying this formula to our equation:

• a = 5
• b = 27
• c = -18

Substituting these values into the formula, we obtain:

x = (-27 ± √(27²-4*5*(-18)))/(2*5)

After calculating the discriminant and simplifying, we find the two roots of the polynomial. We then test intervals between and around the roots to determine where the inequality 5x²+27x-18≤0 is satisfied.