Answer:
x = -5, [tex]\frac{1}{2}[/tex]
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 = [tex]\frac{1}{2}[/tex]
and x + 5 = 0
x = -5
Therefore, x = -5, [tex]\frac{1}{2}[/tex] are the solutions.
