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These are quadratic inequalities because the degree is two and contain an inequality symbol
[tex]3 \times 2 + \times + 10 > 0[/tex]
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Sagot :

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Answer:

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Step-by-step explanation:

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Answer:

A quadratic inequality is an equation of second degree that uses an inequality sign instead of an equal sign.

The solutions to quadratic inequality always give the two roots. The nature of the roots may differ and can be determined by discriminant (b2 – 4ac).

The general forms of the quadratic inequalities are:

ax2 + bx + c < 0

ax2 + bx + c ≤ 0

ax2 + bx + c > 0

ax2 + bx + c ≥ 0

Examples of quadratic inequalities are:

x2 – 6x – 16 ≤ 0, 2x2 – 11x + 12 > 0, x2 + 4 > 0, x2 – 3x + 2 ≤ 0 etc.

How to Solve Quadratic Inequalities?

A quadratic inequality is an equation of second degree that uses an inequality sign instead of an equal sign.

Examples of quadratic inequalities are: x2 – 6x – 16 ≤ 0, 2x2 – 11x + 12 > 0, x2 + 4 > 0, x2 – 3x + 2 ≤ 0 etc.

Solving a quadratic inequality in Algebra is similar to solving a quadratic equation. The only exception is that, with quadratic equations, you equate the expressions to zero, but with inequalities, you’re interested in knowing what’s on either side of the zero i.e. negatives and positives.

How Quadratic Equations are Solved by Factorization Method?

Since we know we can similarly solve quadratic inequalities as quadratic equations, it is useful to understand how to factorize the given equation or inequality.

Let’s see a few examples here.

6x2– 7x + 2 = 0

Solution

⟹ 6x2 – 4x – 3x + 2 = 0

Factorize the expression;

⟹ 2x (3x – 2) – 1(3x – 2) = 0

⟹ (3x – 2) (2x – 1) = 0

⟹ 3x – 2 = 0 or 2x – 1 = 0

⟹ 3x = 2 or 2x = 1

⟹ x = 2/3 or x = 1/2

The general forms of the quadratic inequalities are:

ax2 + bx + c < 0

ax2 + bx + c ≤ 0

ax2 + bx + c > 0

ax2 + bx + c ≥ 0

Examples of quadratic inequalities are:

x2 – 6x – 16 ≤ 0, 2x2 – 11x + 12 > 0, x2 + 4 > 0, x2 – 3x + 2 ≤ 0 etc.

Step-by-step explanation:

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