Question

What is the solution to the quadratic inequality?

Answer 1

The solutions to the quadratic equation are [−5/2,1/3]. Option A

How to determine the solution

Given the inequality;

6x^2≥5−13x

First, convert to quadratic equation

$6 {x}^{2} - 5 + 13x \geqslant 0$

No, let's solve the quadratic equation using the factorization method

$6 {x}^{2} + 13x - 5 \geqslant 0$

Multiply 6 by -5 and find two factor that their product equals the number and their sum equal 13. Those two number are + 15 and -2

Substitute as 15x and 5

-2x in the inequality, we have;

$6 {x}^{2} +15x - 2x - 5 \geqslant 0$

Factor the common multipliers

$3x(2x + 5) - 1(2x + 5) \geqslant 0$

We have two expressions, written as;

$(3x - 1) (2x + 5)\geqslant 0$

Let's solve to get the roots of x

$3x+ 1 \geqslant 0$

$x \geqslant 1/3$

$2x + 5 \geqslant 0$

$x \geqslant \frac{ - 5}{2}$

Thus, the solutions to the quadratic equation are [−5/2,1/3]. Option A

Learn more about quadratic equations here:

brainly.com/question/1214333

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