Which kind of equation is 2×2-3x- 5 = 0?
The quadratic equation 2×2-3x- 5 = 0 can be described as thus. The Highest power of the variation (in this instance, x) in a quad equation, which is a polynomial equating of the second degree, is 2. A quadratic equation has the below general form:
- ax^2 + bx + c = 0
In mathematics as also as many other scientific and engineering phases, quadratic equations are normally used. Depends on the discriminant (the number of the square root in the quad formula), they can have zero, one, or two actual answers.
Given Equation:- 2×2-3x- 5 = 0
Solution 2×2-3x- 5 = 0:
Finding the values of x that fulfil the quadratic equation 2x2-3x- 5 = 0 is what we aim to do.
The coefficients are:
- (The coefficient of x2) a = 2
- X has a coefficient of b = -3.
- (The constant term) c = -5
Put the quadratic formula in given eq. 2×2-3x- 5 = 0 to use: The quadratic equation is presented by:
- x = (-b (b2 – 4ac))/(2a)
- Set the coefficients in:
- a = 2, b = -3, c = -5
- Determine the discriminant, which is the value contained in the square root:
- Discriminatory = b2 – 4 ac
- When we change the values, we obtain:
- Discriminant is equal to (-3)2 – 4 * 2 * (-5)
- Discrimination = 9 + 40 = 49
- Use the discriminant to apply the quadratic formula: x = (-(-3) 49) / (2 * 2)
- Reduce: x = (3 49) / 4
- 49 divided by 7 is the square root, simplified.
- The result is: x = (3 + 7) / 4.
Hence, the two potential answers is
- Using the plus symbol, x = (3 + 7) / 4 = 10 / 4 = 2.5
- X=2.5
- The another equation uses the negative sign: x = (3 – 7) / 4 = -4 / 4 = -1
- X=-1
There are two solutions to the quadratic equation, which is x = 2.5 and x = -1. This says that the original equation 2×2- 3x – 5 = 0 would be satisfied when these values are reinstigated. Of course, We will give a more thorough solution of each step in applying the quad formula to answer the quadratic problem 2×2 – 3x – 5 = 0.
Graphical Representation of 2×2-3x- 5 = 0
Another Way to Solve using Quadratic formula x = (-b (b2 – 4ac))/(2a)
Q. Equation: -2×2-3x- 5 = 0
Solution: Step 1 – Determine the coefficients
The coefficients for your equation 2×2 – 3x – 5 = 0 are as follows:
- (The coefficient of x2) a = 2
- x’s coefficient is b = -3.
- The constant term c = -5
Step 2: Put the quadratic formula to use:
An essential tool for resolving equations of the form ax2 + bx + c = 0 is the quadratic formula. It comes from:
- x = (-b (b2 – 4ac))/(2a)
Step 3: Input the coefficients:
Put your equation’s coefficients a, b, and c into the quadratic formula as follows:
- x = (-(-3) ± √((-3)² – 4 * 2 * (-5))) / (2 * 2)
Step 4: Calculate the discriminant:
In the quadratic formula, the discriminant is the value contained in the square root. It is explained as:
Discriminating factor = b2 – 4 ac
When calculating the discriminant, enter the values of a, b, and c as follows:
- Δ = (-3)² – 4 * 2 (-5)
- Δ = 9 + 40
- Δ = 49
Step 5: Use the discriminant and quadratic formula:
You may use the discriminant in the quadratic formula now that you’ve calculated it:
- b = -3 is x’s coefficient.
Simplex the square root of 49 in step 6:
49 has a square root of 49, which is 7. We thus have:
- x = (3 ± 7) / 4
Step 7: Determine the two options:
Now determine x’s two potential values:
- The first instance uses the add sign: x = (3 + 7) / 4 x = 10 / 4 x = 2.5
- The another equation uses the negative sign: x = (3 – 7) / 4 x = -4 / 4 x = -1
Hence, through quadratic formula we gets two valid solutions: x = 2.5 and x = -1.
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