Math / Algebra

QuestionWhat is the product of the roots for the following equation? $-3 x^{2}-14 x+9=0$
Answer 3 $-3$ $-\frac{14}{3}$ $\frac{14}{3}$

Studdy Solution

STEP 1

1. The given equation is a quadratic equation of the form $ax^2 + bx + c = 0$ .
2. The product of the roots of a quadratic equation can be found using the relationship between the coefficients and the roots.

STEP 2

1. Identify the coefficients $a$ , $b$ , and $c$ from the quadratic equation.
2. Use the formula for the product of the roots of a quadratic equation.
3. Calculate the product of the roots.

STEP 3

Identify the coefficients $a$ , $b$ , and $c$ from the equation $-3x^2 - 14x + 9 = 0$ .
Here, $a = -3$ , $b = -14$ , and $c = 9$ .

STEP 4

Use the formula for the product of the roots of a quadratic equation, which is given by:
$\text{Product of roots} = \frac{c}{a}$

STEP 5

Substitute the values of $c$ and $a$ into the formula:
$\text{Product of roots} = \frac{9}{-3}$
Calculate the product:
$\text{Product of roots} = -3$
The product of the roots is $\boxed{-3}$ .

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QuestionWhat is the product of the roots for the following equation? $-3 x^{2}-14 x+9=0$
Answer 3 $-3$ $-\frac{14}{3}$ $\frac{14}{3}$

Studdy Solution

STEP 1

1. The given equation is a quadratic equation of the form $ax^2 + bx + c = 0$ .
2. The product of the roots of a quadratic equation can be found using the relationship between the coefficients and the roots.

STEP 2

1. Identify the coefficients $a$ , $b$ , and $c$ from the quadratic equation.
2. Use the formula for the product of the roots of a quadratic equation.
3. Calculate the product of the roots.

STEP 3

Identify the coefficients $a$ , $b$ , and $c$ from the equation $-3x^2 - 14x + 9 = 0$ .
Here, $a = -3$ , $b = -14$ , and $c = 9$ .

STEP 4

Use the formula for the product of the roots of a quadratic equation, which is given by:
$\text{Product of roots} = \frac{c}{a}$

STEP 5

Substitute the values of $c$ and $a$ into the formula:
$\text{Product of roots} = \frac{9}{-3}$
Calculate the product:
$\text{Product of roots} = -3$
The product of the roots is $\boxed{-3}$ .

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QuestionWhat is the product of the roots for the following equation? −3x2−14x+9=0-3 x^{2}-14 x+9=0−3x2−14x+9=0Answer 3 −3-3−3 −143-\frac{14}{3}−314​ 143\frac{14}{3}314​

Studdy Solution

STEP 1

1. The given equation is a quadratic equation of the form ax2+bx+c=0 ax^2 + bx + c = 0 ax2+bx+c=0.2. The product of the roots of a quadratic equation can be found using the relationship between the coefficients and the roots.

STEP 2

1. Identify the coefficients a a a, b b b, and c c c from the quadratic equation.2. Use the formula for the product of the roots of a quadratic equation.3. Calculate the product of the roots.

STEP 3

Identify the coefficients a a a, b b b, and c c c from the equation −3x2−14x+9=0 -3x^2 - 14x + 9 = 0 −3x2−14x+9=0.Here, a=−3 a = -3 a=−3, b=−14 b = -14 b=−14, and c=9 c = 9 c=9.

STEP 4

Use the formula for the product of the roots of a quadratic equation, which is given by:Product of roots=ca \text{Product of roots} = \frac{c}{a} Product of roots=ac​

STEP 5

Substitute the values of c c c and a a a into the formula:Product of roots=9−3 \text{Product of roots} = \frac{9}{-3} Product of roots=−39​Calculate the product:Product of roots=−3 \text{Product of roots} = -3 Product of roots=−3 The product of the roots is −3 \boxed{-3} −3​.

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QuestionWhat is the product of the roots for the following equation? $-3 x^{2}-14 x+9=0$
Answer 3 $-3$ $-\frac{14}{3}$ $\frac{14}{3}$

1. The given equation is a quadratic equation of the form $ax^2 + bx + c = 0$ .
2. The product of the roots of a quadratic equation can be found using the relationship between the coefficients and the roots.

1. Identify the coefficients $a$ , $b$ , and $c$ from the quadratic equation.
2. Use the formula for the product of the roots of a quadratic equation.
3. Calculate the product of the roots.

Identify the coefficients $a$ , $b$ , and $c$ from the equation $-3x^2 - 14x + 9 = 0$ .
Here, $a = -3$ , $b = -14$ , and $c = 9$ .

Use the formula for the product of the roots of a quadratic equation, which is given by:
$\text{Product of roots} = \frac{c}{a}$

Substitute the values of $c$ and $a$ into the formula:
$\text{Product of roots} = \frac{9}{-3}$
Calculate the product:
$\text{Product of roots} = -3$
The product of the roots is $\boxed{-3}$ .