Multiple choice

If α and β are zeroes of the quadratic polynomial 5x2 - 2x + 18, then find the value of ( 1 α + 1 β ) 2 .

  1. 1 9

  2. 1 81

  3. -1 9

  4. -1 81
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For 5x^2 - 2x + 18, sum of roots alpha + beta = 2/5, product alpha * beta = 18/5. We need (1/alpha + 1/beta)^2 = ((alpha + beta) / (alpha * beta))^2 = ((2/5) / (18/5))^2 = (2/18)^2 = (1/9)^2 = 1/81.

AI explanation

Using the relationships between roots and coefficients for 5x^2 - 2x + 18 = 0, the sum of the roots (alpha + beta) is 2/5 and the product (alpha * beta) is 18/5. The expression (1/alpha + 1/beta)^2 simplifies to ((alpha + beta)/(alpha * beta))^2. Substituting the values gives ((2/5)/(18/5))^2 = (2/18)^2 = (1/9)^2 = 1/81.

Keep practicing — related questions