Given:
Quadratic equation: 2x² + px - 30 = 0
Root: x = 3


Substituting x = 3 into the equation, we get:
2(3)² + p(3) - 30 = 0

Simplifying the equation:
18 + 3p - 30 = 0
3p - 12 = 0
3p = 12
p = 4

Therefore, the value of p is 4.


To find the other root, we can use the quadratic formula:

The quadratic formula states that for a quadratic equation of the form ax² + bx + c = 0, the roots are given by:
x = (-b ± √(b² - 4ac)) / 2a

In our case, the quadratic equation is:
2x² + px - 30 = 0

Comparing this with the general quadratic equation form, we have:
a = 2
b = p
c = -30

Substituting these values into the quadratic formula, we get:
x = (-p ± √(p² - 4(2)(-30))) / (2(2))

Simplifying further:
x = (-p ± √(p² + 240)) / 4

Since we already know one root is x = 3, we can substitute x = 3 into the equation and solve for p:
3 = (-p ± √(p² + 240)) / 4

Multiplying both sides by 4:
12 = -p ± √(p² + 240)

Squaring both sides:
144 = p² + 240

Rearranging the equation:
p² = 144 - 240
p² = -96

Since the value of p² is negative, this means that there is no real value of p that satisfies the equation. Hence, there is no other real root for the quadratic equation 2x² + px - 30 = 0.