What is the solution to the quadratic inequality?

6x2≥5−13x

[−52,13]
left square bracket negative 5 over 2 comma 1 third right square bracket

(−∞,−13]∪[52,∞)
left parenthesis negative infinity comma negative 1 third right square bracket union left square bracket 5 over 2 comma infinity right parenthesis

[−13,52]
left square bracket negative 1 third comma 5 over 2 right square bracket

(−∞,−52]∪[13,∞)

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barackodam barackodam · Answer 1 · 2022-08-27T02:59:50+02:00

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

Given the inequality;

6x^2≥5−13x

First, convert to quadratic equation

[tex]6 {x}^{2} - 5 + 13x \geqslant 0 [/tex]

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

[tex]6 {x}^{2} + 13x - 5 \geqslant 0[/tex]

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;

[tex]6 {x}^{2} +15x - 2x - 5 \geqslant 0[/tex]

Factor the common multipliers

[tex]3x(2x + 5) - 1(2x + 5) \geqslant 0[/tex]

We have two expressions, written as;

[tex](3x - 1) (2x + 5)\geqslant 0[/tex]

Let's solve to get the roots of x

[tex]3x+ 1 \geqslant 0 [/tex]

[tex]x \geqslant 1/3[/tex]

[tex]2x + 5 \geqslant 0[/tex]

[tex]x \geqslant \frac{ - 5}{2} [/tex]

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

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