The Discriminant serves as an important factor within quadratic equations, used to decipher the type of roots. It can be computed using the formula b² - 4ac from the equation ax²+bx+c=0. A positive discriminant suggests the presence of two real and unique roots, if it's zero, it indicates two real and same roots, and negative value implies the roots are complex.
| Topic | Problem | Solution |
|---|---|---|
| None | Discriminant of a quadratic equation Compute the … | Given the quadratic equation \(-2x^2 + 3x + 8 = 0\), we can identify the coefficients as \(a = -2\)… |
| None | (e) Set the value of a to $-2, b$ to 2 , and $c$ … | Given the quadratic function \(f(x) = ax^2 + bx + c\), we are asked to find the number of x-interce… |
| None | (f) Set the value of a to $-2, b$ to 2 , and $c$ … | Given that a = -2, b = 2, and c = -1. |
| None | Determine, without graphing, whether the given qu… | The given function is a quadratic function of the form \(f(x) = ax^2 + bx + c\). |
| None | Answer the questions below about the quadratic fu… | The given function is a quadratic function of the form \(f(x) = ax^2 + bx + c\). The coefficient of… |
| None | Answer the questions below about the quadratic fu… | The given function is a quadratic function of the form \(f(x) = ax^2 + bx + c\), where \(a = -1\), … |
| None | Question 7 (1 point) Use the discriminant to dete… | Given the quadratic equation \(x^{2}+7x-2=0\), we can identify the coefficients as \(a = 1\), \(b =… |
| None | Find all values of $k$ for which the quadratic eq… | Given the quadratic equation \(2x^{2}+7x+k=0\), we need to find all values of \(k\) for which the e… |
| None | 19. Show that the equation $x^{2}-(2 a+b) x+a b=0… | Given the equation \(x^{2}-(2 a+b) x+a b=0\), we need to show that it has real roots for all values… |
| None | 16. For what values of $m$ does the quadratic equ… | Let's calculate the discriminant and set it equal to 0: \(D = b^2 - 4ac = (-4m)^2 - 4(5m - 3)(m + 1… |