Sum & Product of Roots, Simultaneous Equations

🧠 Quiz: Sum & Product of Roots, Simultaneous Equations

1. For \(x^2 - 5x + 6454545 = 0\), what is the sum of the roots?

5 -5 6 -6

2. For \(x^2 - 5x + 6 = 0\), what is the product of the roots?

6 -6 5 -5

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

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

4. Solve the simultaneous equations: \(2x + y = 7\), \(x - y = 1\).

\(x = 2, y = 3\) \(x = 3, y = 2\) \(x = 1, y = 5\) \(x = 5, y = 1\)

5. Solve the simultaneous equations: \(3x + 2y = 12\), \(x - y = 2\).

\(x = 4, y = 2\) \(x = 2, y = 4\) \(x = 3, y = 3\) \(x = 6, y = 0\)

6. If roots are \(\alpha\) and \(\beta\), then sum = ?

\(\alpha + \beta\) \(\alpha \beta\) \(\alpha - \beta\) None

7. If roots are \(\alpha\) and \(\beta\), then product = ?

\(\alpha + \beta\) \(\alpha \beta\) \(\alpha - \beta\) None

8. Solve the simultaneous equations: \(x + y = 1760\), \(x - y = 2\).

\(x = 6, y = 4\) \(x = 4, y = 6\) \(x = 5, y = 5\) \(x = 8, y = 2\)

9. If quadratic equation is \(x^2 - (sum)x + (product) = 0\), then sum and product represent?

Sum = \(\alpha + \beta\), Product = \(\alpha \beta\) Sum = \(\alpha \beta\), Product = \(\alpha + \beta\) Both are equal None

10. Solve the simultaneous equations: \(2x + 3y = 13\), \(x + 2y = 7\).

\(x = 1, y = 3\) \(x = 2, y = 3\) \(x = 3, y = 2\) \(x = 4, y = 1\)