Unit 8 Quadratic Equations Answer Key Pdf (2024)

FAQs

Does the quadratic formula give 2 answers? ›

As we have seen, there can be 0, 1, or 2 solutions to a quadratic equation, depending on whether the expression inside the square root sign, (b [ 2 ] - 4ac), is positive, negative, or zero.

A quadratic equation takes the form ax2 + bx + c = 0 where a, b and c are numbers. The number a cannot be zero.

If b² - 4ac is positive (>0) then we have 2 solutions. If b² - 4ac is 0 then we have only one solution as the formula is reduced to x = [-b ± 0]/2a. So x = -b/2a, giving only one solution. Lastly, if b² - 4ac is less than 0 we have no solutions.

The quadratic formula helps us solve any quadratic equation. First, we bring the equation to the form ax²+bx+c=0, where a, b, and c are coefficients. Then, we plug these coefficients in the formula: (-b±√(b²-4ac))/(2a) . See examples of using the formula to solve a variety of equations.

A quadratic equation with real coefficients can have either one or two distinct real roots, or two distinct complex roots.

No. The number of real roots depends on the discriminant of the quadratic equation. 1) If the discriminant is negative, then the graph of the equation never intersects the x-axis and so NO real roots exist. 2) if the discriminant is equal to zero, then the graph TOUCHES the x-axis (doesn't go through it).

Note that a quadratic equation has repeated root if b*b-4.0*a*c is equal to zero. However, if a is zero, the equation becomes a linear one whose only solution is -c/b if b is not zero. Otherwise, if b is zero, two cases are possible.

Answer: There are various methods by which you can solve a quadratic equation such as: factorization, completing the square, quadratic formula, and graphing. These are the four general methods by which we can solve a quadratic equation.

9th-11th Grade Math - Quadratic Functions.

If the discriminant is negative, then the square root is not a real number. Square roots of negative values require the using of complex numbers. So, there are 2 solutions, that are not real numbers. Or, 2 complex solutions.

What if b 2 4ac 0? ›

The general solution to such an equation is given by the following formula, called the quadratic formula; If b² -4ac > 0, then the equation has two distinct roots. If b² -4ac = 0, then the equation has a double root. If b² -4ac < 0, then the equation has no real solutions.

Step 1: Using inverse operations, move all terms to one side of your equal sign. Step 2: Simplify your equation, and move terms around so that your equation is in the standard form of a quadratic function. Step 3: Now that your equation is in standard form, you can determine the values for a, b, and c.

The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term. The important condition for an equation to be a quadratic equation is the coefficient of x² is a non-zero term (a ≠ 0).

If the value of the discriminant is positive, there are two real solutions for x, meaning the graph of the solution has two distinct x-intercepts. If the value of the discriminant is zero, there is one real solution for x, meaning the graph of the solution has one x-intercept.

The quadratic equation of the standard form ax2+bx+c has two solutions. The solutions or roots of quadratic equations can be positive/negative, same/distinct, and real or imaginary.

0= (x-1)(x+2) has two solutions. 0= (x-1)(x-1) has one unique solution, but two total solutions. every quadratic equation will always have 2 solutions, they just might not be unique or even real numbers.