-2x^(2)+5x=17 Which of the following describes the solutions to the given equation? Choose 1 answer: (A) The equation has two distinct real, rational solutions. B The equation has two distinct real, irrational solutions. (C) The equation has one distinct real solution. (D) The equation has no real solutions.

Move Terms to One Side: Move all terms to one side of the equation to set it equal to zero. -2x^2 + 5x - 17 = 0Determine Discriminant: Determine the discriminant of the quadratic equation to understand the nature of the solutions. The discriminant is given by the formula b^2 - 4ac, where a, b, and c are the coefficients of the terms ax^2 + bx + c = 0. For our equation, a = -2, b = 5, and c = -17. Discriminant = b^2 - 4ac Discriminant = (5)^2 - 4(-2)(-17)Calculate Discriminant: Calculate the discriminant. Discriminant = 25 - 4(2)(17) Discriminant = 25 - 136 Discriminant = -111Analyze Solutions: Analyze the discriminant to determine the nature of the solutions. Since the discriminant is negative (-111), the quadratic equation has no real solutions. It has two complex solutions.

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-2x^(2)+5x=17
Which of the following describes the solutions to the given equation?
Choose 1 answer:
(A) The equation has two distinct real, rational solutions.
B The equation has two distinct real, irrational solutions.
(C) The equation has one distinct real solution.
(D) The equation has no real solutions.

$-2 x^{2}+5 x=17$ $\newline$ Which of the following describes the solutions to the given equation? $\newline$ Choose $1$ answer: $\newline$ (A) The equation has two distinct real, rational solutions. $\newline$ B The equation has two distinct real, irrational solutions. $\newline$ (C) The equation has one distinct real solution. $\newline$ (D) The equation has no real solutions.

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Math Problems

Algebra 1

Find the number of solutions to a linear equation

Full solution

-2 x^{2}+5 x=17

\newline

Which of the following describes the solutions to the given equation?

\newline

Choose

1

answer:

\newline

(A) The equation has two distinct real, rational solutions.

\newline

B The equation has two distinct real, irrational solutions.

\newline

\newline

(D) The equation has no real solutions.

Move Terms to One Side: Move all terms to one side of the equation to set it equal to zero. $\newline$ $-2x^2 + 5x - 17 = 0$
Determine Discriminant: Determine the discriminant of the quadratic equation to understand the nature of the solutions. The discriminant is given by the formula $b^2 - 4ac$ , where $a$ , $b$ , and $c$ are the coefficients of the terms $ax^2 + bx + c = 0$ . $\newline$ For our equation, $a = -2$ , $b = 5$ , and $c = -17$ . $\newline$ Discriminant = $b^2 - 4ac$ $\newline$ Discriminant = $(5)^2 - 4(-2)(-17)$
Calculate Discriminant: Calculate the discriminant. $\newline$ Discriminant = $25 - 4(2)(17)$ $\newline$ Discriminant = $25 - 136$ $\newline$ Discriminant = $-111$
Analyze Solutions: Analyze the discriminant to determine the nature of the solutions. $\newline$ Since the discriminant is negative $-111$ , the quadratic equation has no real solutions. It has two complex solutions.