The roots of the given quadratic equation are (- 11 ± √145)/4. Therefore, m = - 11, n = 145, and p = 4.
What is a quadratic equation?
"A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where 'a' and 'b' are the coefficients, 'x' is the variable, and 'c' is the constant term. The first condition for an equation to be a quadratic equation is the coefficient of x² is a non-zero term(a ≠ 0)."
The given quadratic equation is:
x(- 2x - 11) = - 3
⇒ - 2x² - 11x = - 3
⇒ 2x² + 11x = 3
⇒ 2x² + 11x - 3 = 0
⇒ x = [- 11 ± {√(11²) - 4×2×(- 3)}]/(2 × 2)
⇒ x = [- 11 ± {√121 + 24}]/4
⇒ x = (- 11 ± √145)/4
Therefore, for the given quadratic equation, m = - 11, n = 145, and p = 4.
Learn more about a quadratic equation here: brainly.com/question/27255597
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