Final answer:
To find the roots of the quadratic equation 2r²-9r-22, apply the quadratic formula which results in two roots by evaluating the expression with both plus and minus options for the square root term.
Step-by-step explanation:
To find the roots of the quadratic equation 2r²-9r-22, we use the quadratic formula: x = √(b²-4ac). The given equation is already in the standard quadratic form ar² + br + c = 0, where a = 2, b = -9, and c = -22.
The quadratic formula is x = [-b ± √(b²-4ac)] / (2a). Plugging in the values from our equation, we get:
x = [9 ± √((-9)²-4(2)(-22))] / (2 * 2)
x = [9 ± √(81+176)] / 4
x = [9 ± √(257)] / 4
Therefore, the roots of the equation 2r²-9r-22 can be found by evaluating the expression with both the plus and minus signs.