Track quiz
Keep this table open while you work.
| Idea | How it goes |
|---|---|
| The zero | An input where the value is 0. One substitution tests it. |
| Brackets | (x − p)(x − q) has zeros p and q. Each bracket is 0 at its own zero. |
| The curve | The zeros are the x-coordinates where the curve meets the x-axis. |
| The sum | If ax² + bx + c has zeros, their sum is −b/a. |
| The product | If ax² + bx + c has zeros, their product is c/a. |
| Backwards | Zeros with sum S and product P give x² − Sx + P. |
| The signs | If zeros exist, a positive product means they share a side. A negative product means they sit on opposite sides. |
| Values from S and P | α² + β² = S² − 2P. And 1/α + 1/β = S/P. |
| The cubic | α + β + γ = −b/a. αβ + βγ + γα = c/a. αβγ = −d/a. |
Which input is a zero of x² − 7x + 12?
p(x) = (x + 4)(x − 6). What are its zeros?
A curve touches the x-axis at one point and turns back. How many zeros does it show?
What is the sum of the zeros of 3x² − 12x + 5?
What is the product of the zeros of 2x² + 6x − 8?
Which quadratic has zeros with sum 6 and product 8?
For x² + 9x + 14, we have S = −9 and P = 14. What do the zeros look like?
α and β are the zeros of x² − 6x + 4. What is α² + β²?
What is the product of the zeros of x³ + 2x² − 5x − 6?
Open Chapter 2, Polynomials, in your NCERT book. Read its solved examples as walks you have already taken.
Next: Pair of Linear Equations in Two Variables. Two equations, two letters, one shared answer.