Question

Which is the quadratic equation in standard form which has roots of 7 and 10?

A. x² + 3x + 17 = 0
B. x² − 17x − 70 = 0
C. x² + 17x + 70 = 0
D. x² − 17x + 70 = 0

Answer 1

The quadratic equation in standard form with roots of 7 and 10 is D. x² - 17x + 70 = 0. This equation is formed by performing the multiplication (x - 7)(x - 10), which equals to x² - 17x + 70.

Step-by-step explanation:

The question asks for the quadratic equation in standard form with roots 7 and 10. The standard form of a quadratic equation is given by ax² + bx + c = 0. To find such an equation with given roots, we can use the fact that if p and q are the roots of the quadratic equation, then the equation can be expressed as (x - p)(x - q) = 0. Substituting 7 and 10 as the roots:

• (x - 7)(x - 10) = 0
• x² - 10x - 7x + 70 = 0
• x² - 17x + 70 = 0

The correct quadratic equation in standard form with the roots 7 and 10 is therefore D. x² - 17x + 70 = 0.