Quadratic Equations - One Line Questions
1.
For the quadratic equation ax^2 + bx + c = 0, what is the product of the roots? —
c/a
2.
What is the value of k for which the equation kx^2 - 5x + k = 0 has equal roots? —
±√(5/2)
3.
What is the value of k if the quadratic equation x^2 - kx + 4 = 0 has equal roots? —
±4
4.
The sum of the roots of the equation (x-2)(x+3) = 0 is: —
-1
5.
The product of the roots of the equation (x-2)(x+3) = 0 is: —
-6
6.
Consider the quadratic equation x^2 - 7x + 10 = 0. What is the difference between its roots? —
3
7.
What are the roots of the quadratic equation x^2 - 2x + 5 = 0? —
1 + 2i and 1 - 2i
8.
The equation 3x^2 + 2x - 1 = 0 has roots: —
1/3 and -1
9.
If the roots of the equation x^2 - 7x + k = 0 are 3 and 4, what is the value of k? —
12
10.
If one root of the equation x^2 - 3x + k = 0 is 1, what is the value of k? —
2
11.
The equation 3x^2 - 6x + 2 = 0 has roots α and β. What is the value of α + β? —
2
12.
For the equation x^2 + 4 = 0, what are the roots? —
2i and -2i
13.
The equation (x+1)^2 = 9 is a quadratic equation. What are its roots? —
2 and -4
14.
What are the roots of the quadratic equation x^2 + 4x + 4 = 0? —
-2 and -2
15.
What are the roots of the quadratic equation x^2 - 5x + 6 = 0? —
2 and 3
16.
The equation 3x^2 - 6x + 2 = 0 has roots α and β. What is the value of αβ? —
2/3
17.
What is the discriminant of the quadratic equation 2x^2 + 5x - 3 = 0? —
49
18.
If one root of the quadratic equation x^2 - (k+1)x + 6 = 0 is 2, find the other root. —
3
19.
What is the value of k for which the roots of the equation x^2 - (k+2)x + 3k = 0 are equal? —
6
20.
If one root of the equation x^2 - (a+1)x + 6 = 0 is 2, find the other root. —
3
21.
What is the value of k if the equation x^2 - 4x + k = 0 has roots that are equal? —
4
22.
The sum of the roots of the equation x^2 + 5x + 3 = 0 is: —
-5
23.
If the roots of the equation x^2 - 5x + k = 0 are 2 and 3, what is the value of k? —
6
24.
What is the quadratic equation whose roots are reciprocals of the roots of x^2 - 5x + 6 = 0? —
6x^2 - 5x + 1 = 0
25.
Which quadratic equation has roots -1/2 and 1/3? —
6x^2 + 5x - 1 = 0
26.
Which of the following quadratic equations has roots 1/2 and -1/3? —
6x^2 + 5x - 1 = 0
27.
If the roots of the quadratic equation x^2 - px + 12 = 0 are 3 and 4, what is the value of p? —
7
28.
If x = 2 is a root of 2x^2 - kx + 6 = 0, what is the value of k? —
7
29.
The product of the roots of the equation 2x^2 - 7x + 6 = 0 is: —
3
30.
If one root of the quadratic equation x^2 - 6x + k = 0 is 2, what is the value of k? —
8
31.
If one root of the equation ax^2 + bx + c = 0 is 0, then which coefficient must be zero? —
c
32.
If the roots of ax^2 + bx + c = 0 are a and b, then which of the following is true? —
a + b = -b/a and ab = c/a
33.
In a quadratic equation ax^2 + bx + c = 0, what condition must 'a' satisfy? —
a != 0
34.
What is the standard form of a quadratic equation? —
ax^2 + bx + c = 0
35.
If the roots of x^2 - ax + b = 0 are m and n, then m+n equals: —
a
36.
If the roots of x^2 - ax + b = 0 are m and n, then mn equals: —
b
37.
What is the discriminant of a quadratic equation ax^2 + bx + c = 0? —
b^2 - 4ac
38.
If the roots of the equation x^2 + bx + c = 0 are equal, then: —
b^2 = 4c
39.
If one root of the equation ax^2 + bx + c = 0 is the square of the other, what is the relation between a, b, and c? —
b^3 = a(c - ab)
40.
For the quadratic equation ax^2 + bx + c = 0, what is the sum of the roots? —
-b/a
41.
Which method involves rewriting the quadratic expression as a perfect square? —
Completing the square
42.
Which of the following is a method to solve quadratic equations? —
All of the above
43.
What is the nature of the roots of the equation x^2 + x + 1 = 0? —
Complex conjugate
44.
What is the nature of the roots of the equation 4x^2 - 12x + 9 = 0? —
Real and equal
45.
What is the nature of the roots of the equation 3x^2 - 5x + 2 = 0? —
Real and distinct
46.
If the discriminant (D = b^2 - 4ac) of a quadratic equation is zero (D = 0), what type of roots does it have? —
Two equal real roots
47.
If the discriminant (D = b^2 - 4ac) of a quadratic equation is negative (D < 0), what type of roots does it have? —
No real roots (two complex conjugate roots)
48.
If the discriminant (D = b^2 - 4ac) of a quadratic equation is positive (D > 0), what type of roots does it have? —
Two distinct real roots
49.
Which quadratic equation has roots 5 and -2? —
x^2 - 3x - 10 = 0
50.
The equation x + 1/x = 5 can be written as a quadratic equation. What is it? —
x^2 - 5x + 1 = 0