Question

P^2-p-6=0
what are p value ALL STEPS

Answer 1

Answers: p = 3 or p = -2

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Work Shown

Method 1

p^2 - p - 6 = 0

(p - 3)(p + 2) = 0

p-3 = 0 or p+2 = 0

p = 3 or p = -2

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Method 2

Replace p with x to get the equation x^2 - x - 6 = 0

Compare that to the template ax^2 + bx + c = 0

a = 1, b = -1, c = -6 are plugged into the quadratic formula.

`\text{x} = (-b\pm√(b^2-4ac))/(2a)\\\\\text{x} = (-(-1)\pm√((-1)^2-4(1)(-6)))/(2(1))\\\\\text{x} = (1\pm√(1 + 24))/(2)\\\\\text{x} = (1\pm√(25))/(2)\\\\\text{x} = (1\pm5)/(2)\\\\\text{x} = (1+5)/(2) \ \text{ or } \ \text{x} = (1-5)/(2)\\\\\text{x} = (6)/(2) \ \text{ or } \ \text{x} = (-4)/(2)\\\\\text{x} = 3 \ \text{ or } \ \text{x} = -2\\\\`

Therefore p = 3 or p = -2 are the two answers.

The quadratic formula takes a bit longer, but it is guaranteed to always work. Whereas factoring is a trial-and-error approach which may not always work. Even if it does work, factoring still requires guessing.