Online Test — Quadratic Equations
10 Questions • 15 min • Chapter MCQ
15:00
Question 1 of 10
medium
Which of the following is a quadratic equation?
2x + 3 = 0
\(x^{3} - 2x\) = 0
\(x^{2} + 1\)/x = 0
\(3x^{2} - 5x + 2\) = 0
Explanation: Quadratic means degree 2; option D has \(x^{2}\) term with a=3≠0
Question 2 of 10
medium
For the equation \(2x^{2} - 8x + 6\) = 0, the value of a + b + c is:
0
2
4
6
Explanation: a=2, b=−8, c=6 → 2+(−8)+6=0
Question 3 of 10
medium
Solve by factorization: \(x^{2} - 9x + 18\) = 0
x=3,6
x=2,9
x=1,18
x=−3,−6
Explanation: 3×6=18, 3+6=9 → (x−3)(x−6)=0 → x=3,6
Question 4 of 10
medium
The discriminant of \(x^{2} - 4x + 4\) = 0 is:
0
8
16
−8
Explanation: \(b^{2}-4ac\) = 16−16=0
Question 5 of 10
medium
If the discriminant is negative, the roots are:
Real and distinct
Real and equal
No real roots
One real root
Explanation: D<0 means no real roots (imaginary/complex)
Question 6 of 10
medium
Completing the square for \(x^{2} + 10x\) = 0 requires adding:
25
100
5
20
Explanation: (b/2)\(^{2}\) = (10/2)\(^{2}\) = \(5^{2}\) = 25
Question 7 of 10
medium
The quadratic formula for \(2x^{2} - 5x + 2\) = 0 gives:
x = (5±\(\sqrt{9}\))/4
x = (5±\(\sqrt{41}\))/4
x = (−5±\(\sqrt{9}\))/4
x = (5±\(\sqrt{25}\))/4
Explanation: a=2,b=−5,c=2 → x=[5±\(\sqrt{25−16}\)]/4 = (5±3)/4
Question 8 of 10
medium
Which equation has equal roots?
\(x^{2} - 5x + 6\) = 0
\(x^{2} + 4x + 4\) = 0
\(x^{2} - 3x + 2\) = 0
\(x^{2} - 7x + 12\) = 0
Explanation: D=16−16=0 → equal roots (x+2)\(^{2}\)=0
Question 9 of 10
medium
The roots of \(x^{2} - 3x - 10\) = 0 are:
5,−2
−5,2
5,2
−5,−2
Explanation: (x−5)(x+2)=0 → x=5, x=−2
Question 10 of 10
medium
For what value of k does \(x^{2} + 6x + k\) = 0 have real roots?
k > 9
k < 9
k ≥ 9
k ≤ 9
Explanation: For real roots, D≥0 → 36−4k≥0 → 4k≤36 → k≤9