3x^(2)+ax-5=0 In the given equation, a is a constant. If the equation has the solutions x=-5 and x=(1)/(3), what is the value of a? ◻

Question

3x^(2)+ax-5=0 In the given equation, a is a constant. If the equation has the solutions x=-5 and x=(1)/(3), what is the value of a?  ◻

Bytelearn · Accepted Answer

Given Quadratic Equation: We are given the quadratic equation 3x^2 + ax - 5 = 0 and its solutions x = -5 and x = 1/3. To find the value of a, we can use the fact that if x is a solution to the equation, then substituting x into the equation should result in a true statement.Substitute x = -5: First, let's substitute x = -5 into the equation: 3(-5)^2 + a(-5) - 5 = 0 Calculate the square and multiply by 3: 3(25) - 5a - 5 = 0 75 - 5a - 5 = 0 Combine like terms: 70 - 5a = 0Solve for a using x = -5: Now, let's solve for a using the result from the substitution of x = -5: 70 - 5a = 0 Add 5a to both sides: 70 = 5a Divide both sides by 5: a = 70 / 5 a = 14 This gives us a value for a based on the solution x = -5.Verify using x = 1/3: Next, we need to verify this value of a using the other solution x = 1/3. Substitute x = 1/3 into the original equation: 3(1/3)^2 + a(1/3) - 5 = 0 Calculate the square and multiply by 3: 3(1/9) + (1/3)a - 5 = 0 1/3 + (1/3)a - 5 = 0 Multiply the entire equation by 3 to clear the fractions: 1 + a - 15 = 0 Combine like terms: a - 14 = 0Solve for a using x = 1/3: Now, let's solve for a using the result from the substitution of x = 1/3: a - 14 = 0 Add 14 to both sides: a = 14 This confirms that the value of a is indeed 14, as it satisfies the equation with both given solutions x = -5 and x = 1/3.

$3x^{2}+ax-5=0$ $\newline$ In the given equation, $a$ is a constant. If the equation has the solutions $x=-5$ and $\newline$ $x=\frac{1}{3}$ , what is the value of $a$ ? $\newline$ ◻

Full solution

More problems from Convert an explicit formula to a recursive formula

Related topics

3x2+ax−5=03x^{2}+ax-5=03x2+ax−5=0\newlineIn the given equation, aaa is a constant. If the equation has the solutions x=−5x=-5x=−5 and \newlinex=13x=\frac{1}{3}x=31​, what is the value of aaa?\newline◻

$3x^{2}+ax-5=0$ $\newline$ In the given equation, $a$ is a constant. If the equation has the solutions $x=-5$ and $\newline$ $x=\frac{1}{3}$ , what is the value of $a$ ? $\newline$ ◻