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How to Solve Polynomial Inequalities?

TopAn expression that contains number of terms joined together by mathematical operators is known as polynomial. In case of polynomial expression infinite values are not present. For example: 7xy2 – 3x + 8y3 – 6. Division operator is not used in Polynomials.

If in any polynomial, less than (<), greater than (>), less than equal (≤) to and greater than equal to (≥) sign present then we can say that polynomial has inequality in it. Now we will see how to solve Polynomial Inequalities. Steps to solve a polynomial are shown below:
Step 1: To solve polynomial inequality first check whether polynomial has zero on its right hand side. Suppose we have a polynomial a2 – 3a – 10 < 0.

Step 2: Then find the factors of polynomial inequality if possible. Factors of above polynomial are: (a - 5) (a + 2) < 0.

Step 3: Calculate where the value of polynomial is zero or at which Point we get the value of polynomial as zero. We get two values of polynomial i.e. a = - 2 and a = 5.

Step 4: Then plot the graph of polynomial where value of polynomial is zero.

Step 5: If any of the given point satisfies the inequality then all points satisfy the inequality. In the same way, if any point does not satisfy the inequality then no point in the region satisfies the inequality. This is how we can solve the polynomial inequalities. This is all about polynomial inequality.