can someone help me with steps
0>x^2 +5x-2
0 > x^2 + 5x - 2
We can also rewrite this as
x^2 + 5x - 2 < 0
First thing to do is find the roots of the equation. Since the quadratic equation is not factorable in just one look, we use the quadratic formula:
x = ( -b +/- sqrt(b^2 - 4ac) ) / 2a
Therefore,
x = ( -5 +/- sqrt((-5)^2 - 4(1)(-2)) ) / 2(1)
x = ( -5 +/- sqrt(25 + 8) ) / 2
x = ( -5 +/- sqrt(33) ) / 2
In decimal,
x1 = 0.3729
x2 = -5.3729
Now to check whether the solution lies between these values of x or outside these boundaries, we get a value between 0.3729 and -5.3729 and check if it satisfies the equation. If it is, then the solution is the all values between x1 and x2, otherwise, it's outside.
For instance, we get x = 0 (zero is between the x1 and x2 values), thus
0 > x^2 + 5x - 2
0 > 0^2 + 5(0) - 2
0 > -2
Indeed zero is greater than -2. Therefore, the solution for x is -5.3729 < x < 0.3729
Hope this helps~ :)
You can also note that since the parabola opens upward,
x^2 + 5x - 2 < 0
will be the region between the roots. Don't be afraid to use what you know, even if it's geometric, not algebraic.
Of course! I can help you with that.
To solve the equation x^2 + 5x - 2 = 0, you can follow these steps:
Step 1: Identify the coefficients
The given equation is x^2 + 5x - 2 = 0. Here, the coefficient of x^2 is 1, the coefficient of x is 5, and the constant term is -2.
Step 2: Determine the discriminant
The discriminant is a value that helps determine the nature of the roots of a quadratic equation. It is calculated using the formula: D = b^2 - 4ac.
In this equation, a = 1, b = 5, and c = -2. Substituting these values into the discriminant formula, we get D = (5)^2 - 4(1)(-2) = 25 + 8 = 33.
Step 3: Determine the nature of the roots
The nature of the roots can be determined based on the value of the discriminant (D).
- If D > 0: The equation has two distinct real roots.
- If D = 0: The equation has one real root (a repeated root).
- If D < 0: The equation has no real roots (complex roots).
Since the discriminant (D) in this case is 33, which is greater than 0, the equation has two distinct real roots.
Step 4: Solve the equation using the quadratic formula
The quadratic formula is given by: x = (-b ± √(b^2 - 4ac)) / (2a)
In this equation, a = 1, b = 5, and c = -2. Substituting these values into the quadratic formula, we get:
x = (-5 ± √(5^2 - 4(1)(-2))) / (2(1))
x = (-5 ± √(25 + 8)) / 2
x = (-5 ± √33) / 2
Step 5: Calculate the roots
To find the roots, you need to calculate both the positive and negative square roots of 33.
Positive Root:
x = (-5 + √33) / 2
Negative Root:
x = (-5 - √33) / 2
These are the steps to solve the equation x^2 + 5x - 2 = 0.