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: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.

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DrSlayNPray

X = -5, X = 1/2 Hope this helped!

Answer:

x = -5, \(\frac{1}{2}\)

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 = \(\frac{1}{2}\)

and x + 5 = 0

x = -5

Therefore, x = -5, \(\frac{1}{2}\) are the solutions.

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