Me! its due
: find all values of x such that $2x^2 +9x - 5=0$ . if you find more than one value, then list your solutions in increasing order, separated by commas.

x = -5,

Step-by-step explanation:

The given equation is 2x² + 9x - 5 = 0

We have to find the values of x.

We know that if in a quadratic equation ax²+ bx + c = 0, b²- 4ac > 0 then there will be two real roots of the equation.

In the given equation b²- 4ac = (9)²-4(2)(-5) = 81 + 40

                                                = 212 > 0

So there will be two real roots.

Now we will factorize the given equation.

2x² + 9x - 5 = 0

2x² + 10x - x - 5 = 0

2x(x + 5) - 1(x + 5) = 0

(2x - 1)(x + 5) = 0

So two roots will be 2x - 1 = 0

x =

and x + 5 = 0

x = -5

Therefore, x = -5, are the solutions.

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true

just pick what you think i need more time let me know if this

step-by-step explanation: