Part 1: Which part of the quadratic formula tells you whether the quadratic equation can be solved by factoring and why?
1. −b
2. b2 − 4ac
3. 2a
Part 2: Create your own quadratic equation. Using complete sentences, and your answer from part 1, determine whether your equation can be solved by factoring.
If b^2 - 4ac is a perfect square, then the roots are rational, and the quadratic can be factored.
b^2 - 4ac ==> this is the discriminant
note: for real numbers a, b and c,,
*if b^2 - 4ac < 0 : 2 imaginary roots
*if b^2 - 4ac = 0 : 1 real and distinct root
*if b^2 - 4ac > 0 : 2 real and distinct roots
Part 1: The part of the quadratic formula that tells you whether the quadratic equation can be solved by factoring is 2. b^2 - 4ac. This is known as the discriminant.
The discriminant is the expression under the square root (√) sign in the quadratic formula. It determines the nature of the solutions to the quadratic equation.
If the discriminant is greater than 0 (positive), then the quadratic equation has two distinct real solutions and can be solved by factoring.
If the discriminant is equal to 0, then the quadratic equation has one real solution (also known as a double root) and can still be solved by factoring.
If the discriminant is less than 0 (negative), then the quadratic equation has no real solutions and cannot be solved by factoring.
Part 2: Let's create a quadratic equation. For example, let's say our quadratic equation is 2x^2 + 5x + 3 = 0.
Now, let's determine whether this equation can be solved by factoring. To do that, we need to calculate the discriminant, which is b^2 - 4ac. In this case, a = 2, b = 5, and c = 3.
Substituting these values into the discriminant formula, we get: (5^2) - 4(2)(3) = 25 - 24 = 1.
Since the discriminant is greater than 0 (1 > 0), the equation has two distinct real solutions and can indeed be solved by factoring.