For the expression x² - 7x - 18, what is the product of its roots?

For the expression x² - 7x - 18, what is the product of its roots?

• A. -18
• B. 7
• C. 0
• D. 2

Answer: (A)

To find the product of the roots of the quadratic expression \(x^2 - 7x - 18\), we can use Vieta's formulas. Vieta's formulas relate the coefficients of a polynomial to sums and products of its roots. For a quadratic equation of the form \(ax^2 + bx + c = 0\), where \(a\), \(b\), and \(c\) are constants, the product of its roots (\(r_1\) and \(r_2\)) is given by \(\frac{c}{a}\). In our expression, \(a\) is 1 (the coefficient of \(x^2\)), \(b\) is -7 (the coefficient of \(x\)), and \(c\) is -18 (the constant term). Since \(a = 1\) and \(c = -18\), we can calculate the product of the roots as: \[ r_1 \cdot r_2 = \frac{c}{a} = \frac{-18}{1} = -18. \] Therefore, the product of the roots of the expression \(x^2 - 7x - 18\)

To find the product of the roots of the quadratic expression (x^2 - 7x - 18), we can use Vieta's formulas. Vieta's formulas relate the coefficients of a polynomial to sums and products of its roots.

For a quadratic equation of the form (ax^2 + bx + c = 0), where (a), (b), and (c) are constants, the product of its roots ((r_1) and (r_2)) is given by (\frac{c}{a}). In our expression, (a) is 1 (the coefficient of (x^2)), (b) is -7 (the coefficient of (x)), and (c) is -18 (the constant term).

Since (a = 1) and (c = -18), we can calculate the product of the roots as:

[

r_1 \cdot r_2 = \frac{c}{a} = \frac{-18}{1} = -18.

]

Therefore, the product of the roots of the expression (x^2 - 7x - 18)