Question

Find the sum and the product of the roots ofof each equation. 2x^2-9

Answer 1

The sum of the roots for the equation \(2x^2 - 9 = 0\) is \(0\), and the product of the roots is \(-4.5\).

Step-by-step explanation:

To find the sum and the product of the roots of the equation \(2x^2 - 9\), we first need to set it in the standard quadratic form, which is \(ax^2 + bx + c = 0\).

For the equation \(2x^2 - 9\), we can rewrite it as \(2x^2 - 9 = 0\) to satisfy this form. In this case, \(a = 2\), \(b = 0\) (since there is no \(x\) term), and \(c = -9\).

The sum of the roots of a quadratic equation \(ax^2 + bx + c = 0\) is given by the formula \(-b/a\). The product of the roots is given by \(c/a\). Applying these formulas, we get:

1. Sum of the roots:
text{Sum of roots} = \frac{-b}{a} = \frac{-0}{2} = 0

2. Product of the roots:
\text{Product of roots} = \frac{c}{a} = \frac{-9}{2} = -4.5

Therefore, the sum of the roots for the equation \(2x^2 - 9 = 0\) is \(0\), and the product of the roots is \(-4.5\).

Answer 2

The sum of the roots of the equation 2x^2 - 9 = 0 is 0, and the product of the roots is -4.5 when rewritten in the standard quadratic form.

Step-by-step explanation:

To find the sum and product of the roots of a quadratic equation of the form ax2+bx+c = 0, you can use the relationships derived from Vieta's formulas. The sum of the roots (α + β) is equal to -b/a, and the product of the roots (α⋅β) is c/a. In the case of the equation 2x2 - 9 = 0, this does not represent a standard quadratic equation since it lacks the bx and c components. However, if we rewrite it as 2x2 + 0x - 9 = 0, we can still apply the relationships: the sum of roots would be 0/2 = 0, and the product would be (-9)/2 = -4.5.