Quadratic Basics: 17 flashcards
All 17 flashcards from this kit, free and with no sign-up.
1. What is the standard form of a quadratic equation in one variable?
Show the answer
$ax^2 + bx + c = 0$, where $a \neq 0$ and $a, b, c$ are real numbers.
2. Which of the following is a quadratic equation? (i) $x^2 + 2x + 1 = 0$ (ii) $x^3 + x = 0$ (iii) $2x + 5 = 0$
Show the answer
Only (i) is quadratic because its highest power of the variable is 2.
3. Define the root (or solution) of a quadratic equation.
Show the answer
A root is a value of the variable that satisfies the equation, i.e., makes the left-hand side equal to zero.
4. How many roots does a quadratic equation have?
Show the answer
A quadratic equation has at most two roots (real or complex).
5. What does it mean to factorize a quadratic expression like $x^2 + 5x + 6$?
Show the answer
It means writing it as a product of two linear factors: $(x + 2)(x + 3)$.
6. Factorize: $x^2 - 5x + 6$.
Show the answer
$(x - 2)(x - 3)$
7. Solve by factorization: $x^2 - 9 = 0$.
Show the answer
$x = 3$ or $x = -3$ (since $(x - 3)(x + 3) = 0$).
8. What is the zero-product property used in solving quadratic equations by factorization?
Show the answer
If $ab = 0$, then either $a = 0$ or $b = 0$ (or both).
9. Solve: $x^2 - 4x = 0$.
Show the answer
$x = 0$ or $x = 4$ (factor out $x$: $x(x - 4) = 0$).
10. Write the quadratic equation whose roots are 2 and 3.
Show the answer
$x^2 - 5x + 6 = 0$ (since $(x - 2)(x - 3) = 0$).
11. What is the condition for a quadratic equation to have real and equal roots?
Show the answer
The discriminant $b^2 - 4ac = 0$.
12. For the equation $x^2 + 4x + 4 = 0$, find the discriminant and the nature of roots.
Show the answer
Discriminant = $4^2 - 4(1)(4) = 0$, so roots are real and equal (both -2).
13. Solve by factorization: $2x^2 - 5x + 2 = 0$.
Show the answer
$x = 2$ or $x = \frac{1}{2}$ (factor as $(2x - 1)(x - 2) = 0$).
14. What is the quadratic formula for solving $ax^2 + bx + c = 0$?
Show the answer
$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
15. Using the quadratic formula, solve $x^2 - 2x - 3 = 0$.
Show the answer
$x = 3$ or $x = -1$ (since $x = \frac{2 \pm \sqrt{4 + 12}}{2} = \frac{2 \pm 4}{2}$).
16. For a quadratic equation, what does the discriminant $b^2 - 4ac$ tell you?
Show the answer
It indicates the nature of roots: positive → two distinct real roots, zero → one real repeated root, negative → no real roots (complex).
17. Find the value of $k$ for which $x^2 + kx + 9 = 0$ has real and equal roots.
Show the answer
$k = \pm 6$ (since discriminant $k^2 - 36 = 0$).
Your notes can be a kit like these
Every kit here was made from real study material. Point Veda at a chapter, a PDF, a photo or a link and get notes, flashcards, practice MCQs, games and a scored test — free, in 42 languages.
- Chapter notes
- Flashcards
- Practice MCQs
- Scored tests
- Exam prep
Get Veda free See what students get
Free to start · No ads · Works in 42 languages