Multiple choice

Sum and product of the zeroes a quadratic polynomial are given. Find the zeroes of the polynomial by factorisation. $\dfrac{-3}{2\sqrt{5}},-\dfrac{1}{2}$

  1. $\dfrac{\sqrt{5}}{3},\dfrac{-\sqrt{5}}{2}$
  2. $\dfrac{\sqrt{5}}{5},\dfrac{-\sqrt{5}}{2}$
  3. $\dfrac{\sqrt{5}}{7},\dfrac{-\sqrt{5}}{2}$
  4. $\dfrac{\sqrt{5}}{6},\dfrac{-\sqrt{5}}{2}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Sum = -3/(2*sqrt(5)), Product = -1/2. The quadratic is x^2 - (sum)x + (product) = 0. x^2 + (3/(2*sqrt(5)))x - 1/2 = 0. Roots are given by quadratic formula. Testing option B: sum = sqrt(5)/5 - sqrt(5)/2 = (2*sqrt(5) - 5*sqrt(5))/10 = -3*sqrt(5)/10 = -3/(2*sqrt(5)). Product = (sqrt(5)/5) * (-sqrt(5)/2) = -5/10 = -1/2.

AI explanation

Let the zeroes be alpha and beta. We check the sum and product for the pair sqrt(5)/5 and -sqrt(5)/2. Their product is (sqrt(5)/5) * (-sqrt(5)/2) = -5/10 = -1/2, and their sum is (2*sqrt(5) - 5*sqrt(5)) / 10 = -3*sqrt(5)/10, which equals -3 / (2*sqrt(5)). The result is sqrt(5)/5 and -sqrt(5)/2.

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