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 ?

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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 ?

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Use Substitution Method: We will use the fact that if x = -5 and x = 1/3 are solutions to the equation 3x^2 + ax - 5 = 0, then they must satisfy the equation when substituted for x. First, let's substitute x = -5 into the equation. 3(-5)^2 + a(-5) - 5 = 0Calculate for x = -5: Calculate the square of -5 and multiply by 3. 3(25) + a(-5) - 5 = 0 75 - 5a - 5 = 0Combine Like Terms: Combine like terms. 70 - 5a = 0Solve for a: Add 5a to both sides to solve for a. 70 = 5aCheck x = 1/3: Divide both sides by 5 to find the value of a. a = 70 / 5 a = 14Calculate for x = 1/3: Now, let's check the second solution x = 1/3 by substituting it into the original equation to ensure it satisfies the equation with a = 14. 3(1/3)^2 + 14(1/3) - 5 = 0Combine Like Terms: Calculate the square of 1/3 and multiply by 3. 3(1/9) + 14/3 - 5 = 0 1/3 + 14/3 - 5 = 0Simplify and Verify: Combine like terms. (1 + 14)/3 - 5 = 0 15/3 - 5 = 0Final Solution: Simplify the fraction and subtract 5. 5 - 5 = 0 0 = 0Since both solutions satisfy the equation with a = 14, we have found the correct value of a.

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

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