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اختبار اختيار من متعدد تفاعلي: Complex Numbers and Quadratic Functions ريفيل
A comprehensive set of questions focusing on operations with complex numbers and the discriminant of quadratic equations.
🏆 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.
Simplify: $\sqrt{-23} \cdot \sqrt{-46}$
A
$23\sqrt{2}$
B
$-23\sqrt{2}$
C
$23i\sqrt{2}$
D
-46i
Explanation
$\sqrt{-23} = i\sqrt{23}$ and $\sqrt{-46} = i\sqrt{46}$. Their product is $i^2 \sqrt{23 \cdot 46} = -1 \sqrt{23 \cdot 2 \cdot 23} = -23\sqrt{2}$.
Simplify: $(3i)(-2i)(5i) = ?$
Explanation
(3 × -2 × 5)(i × i × i) = -30 i3 = -30(-i) = 30i .
Simplify: $i^{11} = ?$
Explanation
i11 = (i4 )2 × i3 = 1 × -i = -i .
Simplify: $(4i)(-6i)^2 = ?$
A
144
B
144i
C
-144
D
-144i
Explanation
(4i)(36i2 ) = (4i)(-36) = -144i .
Simplify: $(6 - 3i) + (4 - 2i) = ?$
A
10 - 5i
B
2 + 5i
C
2 - 5i
D
10 + 5i
Explanation
Combine real and imaginary parts: (6+4) + (-3-2)i = 10 - 5i .
Simplify: $(-11 + 4i) - (1 - 5i) = ?$
A
-12 + 9i
B
-10 - i
C
-12 - 9i
D
-10 + 9i
Explanation
(-11 - 1) + (4 - (-5))i = -12 + 9i .
Simplify: $(5 - 2i)(4 - i) = ?$
A
22 - 13i
B
18 - 13i
C
20 - 2i
D
18 + 13i
Explanation
20 - 5i - 8i + 2i2 = 20 - 13i - 2 = 18 - 13i .
How many real roots does x2 - 8x + 16 = 0 have?
A
One repeated real root
B
Two distinct real roots
C
No real roots
D
Two imaginary roots
Explanation
The discriminant D = b2 - 4ac = (-8)2 - 4(1)(16) = 64 - 64 = 0 . A discriminant of 0 means one repeated real root.
What is the discriminant of x2 - 11x - 26 = 0 ?
A
225
B
121
C
-225
D
-121 + 104
Explanation
D = (-11)2 - 4(1)(-26) = 121 + 104 = 225 .
How many real roots does x2 - 11x - 26 = 0 have?
A
One repeated real root
B
Two distinct real roots
C
No real roots
D
Two imaginary roots
Explanation
Since the discriminant is 225 (positive), there are two distinct real roots.
What is the discriminant of 5x2 - 6 = 0 ?
Explanation
a = 5, b = 0, c = -6 . D = 02 - 4(5)(-6) = 120 .
What type of roots does 5x2 - 6 = 0 have?
A
Two rational real roots
B
One real root
C
Two irrational real roots
D
Two imaginary roots
Explanation
The discriminant is 120, which is positive but not a perfect square, resulting in two irrational real roots.
What is the discriminant of x2 + 8x + 13 = 0 ?
A
12
B
64
C
-12
D
-64 + 52
Explanation
D = 82 - 4(1)(13) = 64 - 52 = 12 .
What type of roots does x2 + 8x + 13 = 0 have?
A
One real root
B
Two irrational real roots
C
No real roots
D
Two rational real roots
Explanation
The discriminant is 12, which is positive but not a perfect square, indicating two irrational real roots.
Describe the discriminant of the related equation of the graph shown.
A
Negative (discriminant < 0 )
B
Zero (discriminant = 0 )
C
Positive (discriminant > 0 )
D
Cannot be determined
Explanation
The parabola does not intersect or touch the x-axis, which means the quadratic equation has no real roots and the discriminant is negative.
Determine the type and number of roots of the graph shown.
A
One repeated real root
B
Two imaginary roots
C
No real roots
D
Two distinct real roots
Explanation
The vertex of the parabola lies exactly on the x-axis, meaning it touches the axis at one point, which corresponds to one repeated real root.
Describe the discriminant of the related equation of the graph shown.
A
Zero
B
Positive
C
Negative (discriminant < 0 )
D
Cannot be determined
Explanation
The parabola crosses the x-axis at two distinct points, indicating that the equation has two distinct real roots and a positive discriminant.
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