X^2-14x+3=-10
Ineed to know how to find the discriminant
quadratic formula and by tabe and graph it Please help me
To find the discriminant of a quadratic equation, you need to understand the quadratic formula. Let's start by rearranging the given equation into the standard quadratic form:
x^2 - 14x + 3 = -10
Move the constant term to the right side:
x^2 - 14x + 3 + 10 = 0
Simplify:
x^2 - 14x + 13 = 0
Now we can identify the coefficients of the quadratic equation in the standard form as follows:
a = 1
b = -14
c = 13
The discriminant (D) is found using the formula D = b^2 - 4ac. Let's calculate it step by step:
D = (-14)^2 - 4(1)(13)
D = 196 - 52
D = 144
So, the discriminant of the given equation is 144.
Now, let's proceed with finding the solutions using both the quadratic formula and by using a table and graph.
1. Quadratic Formula:
The quadratic formula is used to find the solutions of the quadratic equation Ax^2 + Bx + C = 0, where A, B, and C are coefficients.
For our equation: x^2 - 14x + 13 = 0
Using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)
Substituting the values of a, b, and c into the formula:
x = (14 ± √(196 - 4(1)(13))) / (2(1))
x = (14 ± √(196 - 52)) / 2
x = (14 ± √144) / 2
x = (14 ± 12) / 2
The two solutions are obtained by substituting the positive and negative square roots:
x1 = (14 + 12) / 2 = 26 / 2 = 13
x2 = (14 - 12) / 2 = 2 / 2 = 1
Therefore, the solutions to the equation x^2 - 14x + 13 = 0 are x = 13 and x = 1.
2. Graph and Table Method:
To graph and table the equation, first, rewrite the equation as y = x^2 - 14x + 13.
You can use graphing software or online tools to plot the graph of the equation or use a table of values to find the corresponding y-values.
For example, you can choose different values of x and substitute them into the equation to obtain the corresponding y-values:
When x = 0, y = 0^2 - 14(0) + 13 = 13
When x = 1, y = 1^2 - 14(1) + 13 = 0
When x = 2, y = 2^2 - 14(2) + 13 = -1
You can continue this process to get more points and then plot them on a graph.
Using either method, you will find that the solutions to the equation x^2 - 14x + 13 = 0 are x = 13 and x = 1.