alleryA quadratic equation can have at most how many roots?
- three
- one
- two
- four
Show answer and solution
Correct answer: C. two
A quadratic (degree 2) equation has at most two roots.
GRE Quadratic Equations — practice questions — page 3
Explore 78 free Quadratic Equations questions in GRE Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
Practise Quadratic Equations with Quill →Quadratic Equations questions and exercises with answers
Showing questions 61–78 of 78.
A quadratic equation can have at most how many roots?Read the answer and worked solution →Which of the following is a quadratic equation?Read the answer and worked solution →For ax² + bx + c = 0 to be a quadratic equation, what condition must hold?Read the answer and worked solution →Is x = 3 a root of the equation x² − 4x + 3 = 0?Read the answer and worked solution →A rectangular field is 5 m longer than it is wide, and its area is 50 m². If the width is x metres, which equation describes x?Read the answer and worked solution →Identify a, b, c in the equation 3x² − 7x + 2 = 0.Read the answer and worked solution →Solve x² − 5x + 6 = 0 by factorisation.Read the answer and worked solution →Solve x² + 7x + 12 = 0.Read the answer and worked solution →Solve 2x² + 7x + 3 = 0.Read the answer and worked solution →Solve x² − 8x + 16 = 0.Read the answer and worked solution →The roots of x² − x − 12 = 0 are:Read the answer and worked solution →A rectangular plot has its length 3 m more than its width, and its area is 54 m². Find its width.Read the answer and worked solution →For ax² + bx + c = 0, the discriminant is:Read the answer and worked solution →For x² + 4x + 13 = 0, find the discriminant and classify roots.Read the answer and worked solution →For x² − 6x + 9 = 0, find D and the nature of roots.Read the answer and worked solution →Solve 2x² − 5x + 3 = 0 by the quadratic formula.Read the answer and worked solution →For what value of k does x² + kx + 16 = 0 have equal roots?Read the answer and worked solution →Solve x² − 2x − 4 = 0.Read the answer and worked solution →
Worked practice questions
Which of the following is a quadratic equation?
- x³ + x + 1 = 0
- x + 1/x − 2 = 0
- x² − 4x + 4 = 0
- 2 · x + 5 = 0
Show answer and solution
Correct answer: C. x² − 4x + 4 = 0
Quadratic means highest power is exactly 2. Option A is linear. C is cubic.
D is not a polynomial in standard form. Only B fits.
For ax² + bx + c = 0 to be a quadratic equation, what condition must hold?
- a > 0
- a < 0
- a = 1
- a ≠ 0
Show answer and solution
Correct answer: D. a ≠ 0
If a = 0 the x² term disappears and the equation becomes linear.
The only requirement is a ≠ 0.
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