Question

5/5
Write a Quadratic equation in Standard Form, whose solutions are 7 and 3.
y = x ^ 2 + 10x - 21
y = x ^ 2 - 10x + 21
y = x ^ 2 + 10x + 21
y = x ^ 2 - 10x - 21

Answer 1

To find a quadratic equation in standard form given its solutions (roots) of 7 and 3, we can use the fact that if \( r_1 \) and \( r_2 \) are the roots of the quadratic equation, it can be expressed as:

\[
y = k(x - r_1)(x - r_2)
\]

where \( k \) is a constant (usually taken as 1 for simplicity when looking for the standard form).

In this case, the roots are 7 and 3, so we have:

\[
y = (x - 7)(x - 3)
\]

Now, expand this:

\[
y = x^2 - 3x - 7x + 21
\]
\[
y = x^2 - 10x + 21
\]

Thus, the quadratic equation in standard form is:

\[
y = x^2 - 10x + 21
\]

From the provided options, the correct answer is:

**y = x² - 10x + 21**