Discriminant of a Quadratic Equation - Definition & Examples
Read this topicExplanations 3
- The Discriminant When does ax2+bx+c=0ax^2+bx+c=0ax2+bx+c=0 have a real solution? Well, we know how to find the solutions using the quadratic formula: x=−b±b2−4ac2a.x = \frac{-b …
By Moor Xu, Victor Wang, Catherine Yeo, Victor Wang, Jonathan Heller, Gabi Slizewska, Anusha Rahman, Caroline K
- (Video) The Discriminant by Eddie Woo This video by Eddie Woo explains the discriminant. Summary\large{\text{Summary}}Summary The discriminant is the part of the quadratic formu…
By Alex Federspiel, Victor Wang, Amy Feraco, Jonathan Heller, Caroline K, Anusha Rahman
- Discriminant Let's do a little review before we investigate the discriminant. Given a quadratic equation in standard form, ax2+bx+c=0,ax^2+bx+c=0,ax2+bx+c=0, where a,b,a, b,a,b,…
By Caroline K, Anusha Rahman
Problems 26
- Find the discriminant of 2x2+6x−32x^2 + 6x - 32x2+6x−3.
- What is the discriminant of the quadratic 9x2−30x+259x^2 -30x + 259x2−30x+25?
- Compute the discriminant of 5x2+7x−35x^2 +7 x - 35x2+7x−3.
- What is the discriminant of the quadratic 13x2+4x+3\frac{1}{3}x^2+4x+331x2+4x+3? Does this mean that the roots are real or non-real?
- What is the discriminant of x2−3xx^2-3xx2−3x?
- What is the discriminant of 2x2+5x−22x^2+5x-22x2+5x−2?
- What is the discriminant of 32x2−7x+8\frac{3}{2}x^2-7x+823x2−7x+8?
- If the discriminant is a negative number, the root(s) will be:
- What is the largest possible value of the discriminant of the quadratic (x−r)(x−r−2)(x-r)(x-r-2)(x−r)(x−r−2), as rrr varies over the real numbers?
- What is the largest possible value of the discriminant of the quadratic (x−r)(x−r−2)(x-r)(x-r-2)(x−r)(x−r−2), as rrr varies over the complex numbers?
- Galois is trying to write questions for his algebra class with nice answers without radicals. He finds a list of quadratics ax2+bx+cax^2 + bx + cax2+bx+c with integer coefficien…
- Choose the fewest pieces of information below that can be used to determine the discriminant of a quadratic ax2+bx+cax^2+bx+cax2+bx+c.
- A quadratic polynomial ax2+4x−6ax^2 + 4x - 6ax2+4x−6 has discriminant −8-8−8. Find aaa.
- The quadratic polynomial 3x2−2x+c3x^2 -2x + c3x2−2x+c has discriminant −20-20−20. Find ccc.
- Use the discriminant to determine which of the following equations have 222 real solutions. (Select all that apply.)
- Use the discriminant to determine which of the following equations have 222 real solutions. (Select all that apply.)
- For a general quadratic equation in standard form ax2+bx+c=0ax^2+bx+c=0ax2+bx+c=0, what is the maximum value that aaa can be for the equation to have at least one real solution,…
- For a general quadratic equation in standard form ax2+bx+c=0ax^2+bx+c=0ax2+bx+c=0, what is the maximum value that ccc can be for the equation to have at least one real solution,…
- For a general quadratic equation in standard form ax2+bx+c=0ax^2+bx+c=0ax2+bx+c=0, what is the range of values that bbb can be for the equation to have at least one real solutio…
- If f(x)=ax2+4x−2f(x)=ax^2+4x-2f(x)=ax2+4x−2 is a quadratic function with at least one real zero, what is the minimum value that aaa can be?
- If f(x)=2x2+bx+2f(x)=2x^2+bx+2f(x)=2x2+bx+2 is a quadratic function with at least one real zero, which of the following are possible values for bbb? (Select all that apply.)
- If f(x)=2x2−4x+cf(x)=2x^2-4x+cf(x)=2x2−4x+c is a quadratic function with at least one real zero, what is the maximum value that ccc can be?
- Concept check: If a quadratic equation has zero real-numbered solutions, which of the following must be true of the discriminant Δ\DeltaΔ?
- If a quadratic ax2+bx+cax^2+bx+cax2+bx+c factors as a perfect square, (Ax+B)2(Ax+B)^2(Ax+B)2, then its discriminant must be...
- Let fff and ggg be polynomials with degree at most 222 that have the same discriminant and the same linear coefficient. If ggg has 000 as an xxx-intercept, then which of the fol…
- The circle with equation (x−1)2+y2=4(x - 1)^2 + y^2 = 4(x−1)2+y2=4 intersects the parabola y=x2−2x+3y = x^2 - 2x + 3y=x2−2x+3 in one location on the real xyxyxy plane. Which of …