NCERT · Class 10 · Mathematics · PolynomialsIf the product of zeroes of the quadratic polynomial $ax^2 - 6x - 6$ is 4, find the value of $a$.

Consider the given quadratic polynomial $p(x) = ax^2 - 6x - 6$. Comparing this with the general quadratic expression $Ax^2 + Bx + C$, we can clearly identify the respective coefficients: $A = a$, $B = -6$, and $C = -6$. According to the relationship between the coefficients and zeroes of a quadratic polynomial, the product of the zeroes is given by the ratio of the constant term to the leading coefficient, which is $C/A$. Here, the product of zeroes is given as 4. Therefore, we can set up the equation $-6/a = 4$. Solving this equation for $a$, we get $4a = -6$, which means $a = -6/4$, simplifying to $a = -3/2$.