Question

Write the quadratic equation whose roots are α and β and whose leading coefficient is k.

a) k(x - α)(x - β)
b) k(x + α)(x + β)
c) k(x - α)(x + β)
d) k(x + α)(x - β)

Answer 1

The correct quadratic equation is option (d) k(x + α)(x - β).

Step-by-step explanation:

The quadratic equation whose roots are α and β and whose leading coefficient is k is given by option (d) k(x + α)(x - β).

Let's break down the options:

1. a) k(x - α)(x - β)
2. b) k(x + α)(x + β)
3. c) k(x - α)(x + β)
4. d) k(x + α)(x - β)

In option a), the signs inside the parentheses are both negative which would result in a positive value when multiplied, however, the quadratic equation should have a negative constant term since c < 0. So, option a) is not the correct choice.

In option b), the signs inside the parentheses are both positive which would also result in a positive value when multiplied, so option b) is not the correct choice.

In option c), the first parentheses has a negative sign and the second parentheses has a positive sign. When multiplied, this would give a negative value which is correct, so option c) is closer to the correct solution.

However, the correct answer is option d) k(x + α)(x - β). In this option, the first parentheses has a positive sign and the second parentheses has a negative sign. When multiplied, this would give a negative value, which is the correct sign for the quadratic equation's constant term.