If the product of the zeroes of the quadratic polynomial p(x)=ax^(2)-6x-6 is 4 , then find the value of a. Also, find the sum of the zeroes of the polynomial.

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Denote the zeroes: Let's denote the zeroes of the polynomial p(x) = ax^2 - 6x - 6 as α (alpha) and β (beta). According to Vieta's formulas, for a quadratic polynomial ax^2 + bx + c, the product of the roots is given by c/a and the sum of the roots is given by -b/a.Use Vieta's formula: Given that the product of the zeroes (αβ) is 4, we can write the equation using Vieta's formula: αβ = c/a. In our case, c = -6 and we are given αβ = 4. So we have -6/a = 4.Solve for a: Solving for a, we multiply both sides by a to get -6 = 4a. Then, we divide both sides by 4 to find the value of a: a = -6/4 = -3/2.Find sum of zeroes: Now, we need to find the sum of the zeroes (α + β). Using Vieta's formula again, we have α + β = -b/a. In our case, b = -6 and we have already found a = -3/2. So we have α + β = -(-6)/(-3/2).Simplify the expression: Simplifying the expression for the sum of the zeroes, we get α + β = 6/(-3/2) = 6 * (-2/3) = -4.

If the product of the zeroes of the quadratic polynomial $p(x)=a x^{2}-6 x-6$ is $4$ , then find the value of $a$ . Also, find the sum of the zeroes of the polynomial.

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If the product of the zeroes of the quadratic polynomial p(x)=ax2−6x−6 p(x)=a x^{2}-6 x-6 p(x)=ax2−6x−6 is 444 , then find the value of a a a. Also, find the sum of the zeroes of the polynomial.

If the product of the zeroes of the quadratic polynomial $p(x)=a x^{2}-6 x-6$ is $4$ , then find the value of $a$ . Also, find the sum of the zeroes of the polynomial.