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Interactive multiple-choice quiz: Quadratic Formula & The Discriminant Worksheet - Reveal
This worksheet focuses on the quadratic formula and the discriminant. It includes questions on identifying the discriminant formula, determining the number and type of roots based on the discriminant value, and solving various quadratic equations. Students will practice working with real and imaginary roots, as well as understanding the graphical significance of setting quadratic equations to zero to find x-intercepts.
🏆 انضم إلى التحدي واحصل على ترتيبك
اختبار شهادة تدريبي مؤقت للصف والمادة والفصل نفسه.
ابدأ السباق ✨
اختر إجابة واحدة لكل سؤال. عند الاختيار ستظهر النتيجة فورًا: الأخضر صحيح، والأحمر خطأ، وسيظهر تفسير الإجابة مباشرة إن كان متوفرًا. وبعد آخر سؤال ستظهر الدرجة النهائية تلقائيًا.
🚩 Report
The discriminant is
A
ax2 + bx + c
B
b - 4ac
C
b2 - 4ac
D
b2 + 4ac
Explanation
The discriminant of a quadratic equation in the form ax2 + bx + c = 0 is defined as b2 - 4ac .
🚩 Report
Determine the value of the discriminant and describe the number and type roots for the following: x2 + 7x + 13
A
101; 2 real roots
B
3; 2 real roots
C
-101; 2 imaginary roots
D
-3; 2 imaginary roots
Explanation
For the equation x2 + 7x + 13 , a=1, b=7, c=13 . The discriminant is b2 - 4ac = 72 - 4(1)(13) = 49 - 52 = -3 . Since the discriminant is negative, there are two imaginary roots.
🚩 Report
Use the quadratic formula to solve 2x2 + 2x - 12 .
A
x = -2, 3
B
x = 2, 3
C
x = 2, -3
D
x = -2, -3
Explanation
Simplifying 2x2 + 2x - 12 = 0 by dividing by 2 gives x2 + x - 6 = 0 . Factoring gives (x+3)(x-2) = 0 , so x = 2 and x = -3 .
🚩 Report
If the discriminant is negative, then the quadratic has:
A
1 Real Solution
B
2 Real Solutions
C
Half a Solution
D
2 Complex (imaginary) Solutions
Explanation
A negative discriminant means the term under the square root in the quadratic formula is negative, resulting in two complex (imaginary) solutions.
🚩 Report
The quadratic equation can be used to solve quadratic equations that can or cannot be factored.
Explanation
The quadratic formula is a universal method that can solve any quadratic equation, whether it is factorable or not.
🚩 Report
Solve the equation
2p2 - 3p - 3 = 0 using the Quadratic Formula.
A
\(\frac{3 \pm \sqrt{33}}{4}\)
B
\(\frac{-1 \pm \sqrt{13}}{2}\)
C
{2, 1}
D
\(\frac{3 \pm \sqrt{17}}{2}\)
Explanation
Using the formula \(\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\) with a=2, b=-3, c=-3 : \(\frac{3 \pm \sqrt{(-3)^2 - 4(2)(-3)}}{2(2)} = \frac{3 \pm \sqrt{9 + 24}}{4} = \frac{3 \pm \sqrt{33}}{4}\).
🚩 Report
Solve using the quadratic formula: f(x) = 2x2 - 4x + 7
A
\(x = (2 \pm 2i\sqrt{10})/2\)
B
\(x = (4 \pm \sqrt{40})/4\)
C
\(x = (2 \pm i\sqrt{10})/2\)
D
\(x = (2 \pm 2i\sqrt{40})/4\)
Explanation
For 2x2 - 4x + 7 = 0 , roots are \(\frac{4 \pm \sqrt{16 - 56}}{4} = \frac{4 \pm \sqrt{-40}}{4} = \frac{4 \pm 2i\sqrt{10}}{4} = \frac{2 \pm i\sqrt{10}}{2}\).
🚩 Report
If the discriminant is equal to 0, how many solutions are there?
A
No solutions
B
1 Solution
C
2 Solutions
D
Infinite solutions
Explanation
When the discriminant is zero, the quadratic equation has exactly one real solution (a repeated root).
🚩 Report
If the discriminant is equal to 4, how many solutions are there?
A
No Solutions
B
1 Solution
C
2 Solutions
D
Infinite Solutions
Explanation
When the discriminant is positive, the quadratic equation has two distinct real solutions.
🚩 Report
Solve the equation
x2 - x - 2 = 0 using the Quadratic Formula.
A
\(\frac{-1 \pm \sqrt{10}}{3}\)
B
{2, -1}
C
{2, -3}
D
{1, -2}
Explanation
Factoring x2 - x - 2 = 0 gives (x-2)(x+1) = 0 , resulting in roots x=2 and x=-1 .
🚩 Report
Use the quadratic formula to determine the solutions to the equation 2x2 - 9x - 35 = 0 .
A
x = 7/2, x = -6
B
x = -5/2, x = 5
C
x = -3/7, x = 6
D
x = -5/2, x = 7
Explanation
Using the quadratic formula: \(x = \frac{9 \pm \sqrt{81 - 4(2)(-35)}}{4} = \frac{9 \pm \sqrt{361}}{4} = \frac{9 \pm 19}{4}\). Solutions are 28/4 = 7 and -10/4 = -5/2 .
🚩 Report
Solve x2 - 5x + 10 = 0 .
A
\(x = (5 - i\sqrt{15})/2, (5 + i\sqrt{15})/2\)
B
\(x = (5 - \sqrt{15})/2, (5 + \sqrt{15})/2\)
C
\(x = (5 - i\sqrt{65})/2, (5 + i\sqrt{65})/2\)
D
\(x = (5 - \sqrt{65})/2, (5 + \sqrt{65})/2\)
Explanation
The discriminant is 25 - 40 = -15 . Roots are \(\frac{5 \pm \sqrt{-15}}{2} = \frac{5 \pm i\sqrt{15}}{2}\).
🚩 Report
Solve for x : 3x2 - 6x + 6 = 0
A
\(x = 1 \pm i\)
B
x = 3, -6
C
x = 4.8, 2.7
D
Undefined
Explanation
Divide by 3 to get x2 - 2x + 2 = 0 . The discriminant is 4 - 8 = -4 . Roots are \(\frac{2 \pm \sqrt{-4}}{2} = \frac{2 \pm 2i}{2} = 1 \pm i\).
🚩 Report
Solve 2x2 - 36 = x
A
\(x = \frac{-9}{2}\) and 4
B
\(x = \frac{9}{2}\) and -4
C
x = 4 and -4
D
No real solution
Explanation
Rewrite as 2x2 - x - 36 = 0 . Using formula: \(x = \frac{1 \pm \sqrt{1 - 4(2)(-36)}}{4} = \frac{1 \pm 17}{4}\). Solutions are 18/4 = 4.5 and -16/4 = -4 .
🚩 Report
Why are quadratic equations set equal to zero?
A
Because zero is an easy number to work with.
B
Because we are trying to find the x-intercepts and that happens when y = 0 .
C
Because setting it equal to zero helps us find the y-intercepts.
D
None of the above
Explanation
Setting a quadratic function equal to zero allows us to solve for x values where the graph intersects the horizontal axis (x-intercepts).
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