Sum and Product of Roots

🧠 Quiz: 3.5 Sum and Product of Roots

1. For \(ax^2 + bx + c = 0\), the sum of the roots is:

\(-\frac{b}{a}\) \(\frac{b}{a}\) \(-\frac{c}{a}\) \(\frac{c}{a}\)

2. For \(ax^2 + bx + c = 0\), the product of the roots is:

\(\frac{b}{a}\) \(-\frac{b}{a}\) \(\frac{c}{a}\) \(-\frac{c}{a}\)

3. For \(ax^2 + bx + c = 0\) with roots \(\alpha\) and \(\beta\), which relation is true?

\(\alpha + \beta = -\frac{b}{a}\) \(\alpha + \beta = \frac{c}{a}\) \(\alpha\beta = -\frac{b}{a}\) \(\alpha\beta = -\frac{c}{a}\)

4. Which statement correctly links coefficients and the product of the roots?

The product equals \(-\frac{b}{a}\) The product equals \(\frac{c}{a}\) The product equals \(-\frac{c}{a}\) The product equals \(\frac{b}{a}\)

5. If the sum of roots is 7 and product is 10, the quadratic is:

\(x^2 - 7x + 10 = 0\) \(x^2 + 7x + 10 = 0\) \(x^2 - 10x + 7 = 0\) \(x^2 + 10x - 7 = 0\)

6. If roots are \(\alpha, \beta\), then \(\alpha + \beta\) equals:

\(-\frac{b}{a}\) \(\frac{c}{a}\) \(\frac{b}{a}\) \(-\frac{c}{a}\)

7. If roots are \(\alpha, \beta\), then \(\alpha \cdot \beta\) equals:

\(\frac{c}{a}\) \(-\frac{c}{a}\) \(\frac{b}{a}\) \(-\frac{b}{a}\)

8. If the sum of the roots is 4 and product is 4, the quadratic is:

\(x^2 - 4x + 4 = 0\) \(x^2 + 4x + 4 = 0\) \(x^2 - 4x - 4 = 0\) \(x^2 + 4x - 4 = 0\)

9. If the sum of the roots is -5 and product is 6, the quadratic is:

\(x^2 + 5x + 6 = 0\) \(x^2 - 5x + 6 = 0\) \(x^2 + 6x + 5 = 0\) \(x^2 - 6x + 5 = 0\)

10. If the sum of the roots is 0 and product is 9, the quadratic is:

\(x^2 - 9 = 0\) \(x^2 + 9 = 0\) \(x^2 + x - 9 = 0\) \(x^2 - x + 9 = 0\)