Multiple choice

If $\alpha, \beta$ are the zeroes of the quadratic polynomial $f(x)=x^2-5x+4$, then $\dfrac {1}{\alpha}+\dfrac {1}{\beta}-2\alpha \beta=$

  1. $\dfrac {27}{4}$
  2. $-\dfrac {27}{4}$
  3. $\dfrac {4}{27}$
  4. $-\dfrac {4}{27}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For x^2 - 5x + 4 = 0, the sum of roots alpha + beta = 5 and product alpha * beta = 4. The expression 1/alpha + 1/beta - 2*alpha*beta simplifies to (alpha + beta)/(alpha * beta) - 2*alpha*beta, which is 5/4 - 2(4) = 5/4 - 8 = (5 - 32)/4 = -27/4.

AI explanation

From the polynomial f(x) = x^2 - 5x + 4, the sum of the zeroes (alpha + beta) is 5 and the product (alpha * beta) is 4. Substitute these values into the expression 1/alpha + 1/beta - 2*alpha*beta, which simplifies to (alpha + beta) / (alpha * beta) - 2*alpha*beta. Calculating this gives 5/4 - 2(4) = 5/4 - 8 = 5/4 - 32/4 = -27/4.

Keep practicing — related questions