Posted by Tika on Monday, April 27, 2015 at 1:03pm.
How do I write an quadratic equation whose roots are -1 and -2 and whose leading coefficient is 1. Sorry my equal key does not work
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See your previous post.
To write a quadratic equation with roots -1 and -2 and a leading coefficient of 1, you can follow these steps:
Step 1:
Start with the general form of a quadratic equation: ax^2 + bx + c = 0. Since the leading coefficient is given as 1, we know that a = 1.
Step 2:
The roots of a quadratic equation are the values of x where the equation equals zero. In this case, the roots are -1 and -2. So when x = -1, the equation equals zero, and when x = -2, the equation also equals zero.
Step 3:
Substitute the values of the roots into the equation to create two equations. We know that when x = -1, the equation equals zero. Therefore, we have:
1(-1)^2 + b(-1) + c = 0
Simplifying this gives:
1 - b + c = 0
Similarly, when x = -2, the equation equals zero:
1(-2)^2 + b(-2) + c = 0
Simplifying this gives:
4 - 2b + c = 0
Step 4:
Combine the two equations to get a single quadratic equation. Subtract the second equation from the first equation to eliminate the constant term "c":
(1 - b + c) - (4 - 2b + c) = 0
Simplifying this gives:
-3 + b = 0
Step 5:
Finally, write the quadratic equation with the given roots and leading coefficient:
x^2 + (-3)x + 0 = 0
You can express this equation in a readable format:
x^2 - 3x = 0