Multiple choice

For a quadratic polynomial $p(x) = ax^2 + bx + c, \alpha + \beta = 2$ and $\alpha \beta = - 8$ where $\alpha, \beta $ are zeroes of $p(x)$. $\therefore $ The value of $a, b$ and $c$ is ________ respectively.

  1. $a, -2a, - 8a$
  2. $a, 2a, 8a$
  3. $b, b, 4b$
  4. $2b, b, 4b$
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A Correct answer
Explanation

For a quadratic polynomial, the sum of roots is -b/a = 2 and the product is c/a = -8. Thus b = -2a and c = -8a. The coefficients are a, -2a, and -8a.

AI explanation

For a standard quadratic polynomial ax^2 + bx + c, the sum of the zeros is given by -b/a and the product is c/a. We are given the sum alpha + beta = 2, so -b/a = 2, which means b = -2a. We are also given the product alpha*beta = -8, so c/a = -8, meaning c = -8a. The values of a, b, and c are therefore a, -2a, and -8a respectively.