Multiple choice

Verify the quadratic polynomial, for the zeros $\alpha,\beta$ given in each case

  1. $2,-1, \quad x^2-x-2$
  2. $\sqrt{3},-\sqrt{3}, \quad x^2-4$
  3. $\dfrac{1}{4},-1, \quad 4x^2+3x-2$
  4. $\dfrac{1}{2},\dfrac{3}{2}, \quad 4x^2-8x+4$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For zeros 2 and -1, the sum is 1 and the product is -2. The quadratic polynomial is x^2 - (sum)x + (product) = x^2 - x - 2. This matches option A.

AI explanation

Use the sum and product of roots to form the quadratic polynomial with zeroes 2 and -1. The sum of the roots is 1 and the product is -2, which gives the polynomial x^2 - (sum)x + (product) = x^2 - x - 2. Therefore, 2 and -1 are verified as the zeroes for x^2 - x - 2.

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