Finding the Discriminant

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.

The problems about Finding the Discriminant

Topic	Problem	Solution
None	Discriminant of a quadratic equation Compute the …	Given the quadratic equation $- 2 x^{2} + 3 x + 8 = 0$ , 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 $f (x) = a x^{2} + b x + c$ , 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 $f (x) = a x^{2} + b x + c$ .
None	Answer the questions below about the quadratic fu…	The given function is a quadratic function of the form $f (x) = a x^{2} + b x + c$ . The coefficient of…
None	Answer the questions below about the quadratic fu…	The given function is a quadratic function of the form $f (x) = a x^{2} + b x + c$ , where $a = - 1$ , …
None	Question 7 (1 point) Use the discriminant to dete…	Given the quadratic equation $x^{2} + 7 x - 2 = 0$ , we can identify the coefficients as $a = 1$ , \(b =…
None	Find all values of $k$ for which the quadratic eq…	Given the quadratic equation $2 x^{2} + 7 x + k = 0$ , 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…