MP Board · Class 10 · Mathematics · PolynomialsIf $\alpha$ and $\beta$ are the zeroes of $2x^2 - 8x + 6$, find the value of $\alpha + \beta$ and $\alpha \beta$.

Given the quadratic polynomial $p(x) = 2x^2 - 8x + 6$, we can compare it with the standard quadratic form $ax^2 + bx + c$ to identify the coefficients: $a = 2$, $b = -8$, and $c = 6$. According to the relationship between the zeroes and coefficients of a quadratic polynomial, the sum of zeroes is given by the formula $\alpha + \beta = -b/a$. Substituting the values, we get $-(-8)/2 = 8/2 = 4$. Similarly, the product of zeroes is given by $\alpha \beta = c/a$. Substituting the respective values gives $6/2 = 3$. Therefore, $\alpha + \beta = 4$ and $\alpha \beta = 3$.