/20 1234567891011121314151617181920 Test Code: MC2L4 1 / 20 1. If 𝛼 and 𝛽 are the zeros of the quadratic polynomial p(s) = 3s² − 6s + 4, find the value of 𝛼/𝛽 + 𝛽/𝛼 + 2 [1/𝛼 + 1/𝛽] + 3𝛼𝛽 A) 9 B) 0 C) 13 D) 8 📝 Solution: 2 / 20 2. If 𝛼 and 𝛽 are the zeros of the quadratic polynomial f(t) = t² − 4t + 3, find the value of 𝛼⁴𝛽³ + 𝛼³𝛽⁴ A) 108 B) 80 C) 100 D) 105 📝 Solution: 3 / 20 3. If 𝛼 and 𝛽 are the zeros of the quadratic polynomial f(x) = 6×2 + x − 2, find the value of 𝛼/𝛽+𝛽/𝛼 A) 25/15 B) 25/12 C) -25/12 D) 20/12 📝 Solution: 4 / 20 4. If 𝛼 and 𝛽 are the zeros of the quadratic polynomial p(y) = 5y² − 7y + 1, find the value of 1/𝛼 + 1/𝛽 A) 15 B) 14 C) 9 D) 7 📝 Solution: 5 / 20 5. If the squared difference of the zeros of the quadratic polynomial f(x) = x² + px + 45 is equal to 144, find the value of p. A) ±1 B) -7 C) ±12 D) 3/2 📝 Solution: 6 / 20 6. If the zeros of the polynomial f(x) = 2x³ − 15x² + 37x − 30 are in A.P., find them. A) 2, 4/2, 3 B) 2, 5/2, 3 C) 3, 5/2, 5 D) 6/2, 3/2, 3 📝 Solution: 7 / 20 7. If the zeroes of the polynomial 𝑓(𝑥) = 𝑎𝑥³ + 3𝑏𝑥² + 3𝑐𝑥 + 𝑑 are in A.P., prove that 2𝑏³ − 3𝑎𝑏𝑐 + 𝑎²𝑑 = 0 [Select the Sum of Zeroes or Type Your Answer] A) -2b/a B) None of these C) −3𝑏/𝑎 D) -5a/b 📝 Solution: 8 / 20 8. If a and 3 are the zeros of the quadratic polynomial f(x) = x² + x − 2, find the value of 1/𝛼 − 1/𝛽 A) 2/3 B) 4/2 C) 5/3 D) 3/2 📝 Solution: 9 / 20 9. Obtain all zeros of the polynomial f(x) = 2x⁴ + x³ − 14x² − 19x − 6, if two of its zeros are −2 and −1. A) −1, -3, 2, 0 B) None of these C) 2 , 3, −2, 1 D) −1/2 , 3, −2, −1 📝 Solution: 10 / 20 10. If the sum of the zeros of the quadratic polynomial f(t) = kt² + 2t + 3k is equal to their product, find the value of k. A) 3/2 B) -5/4 C) 4/3 D) -2/3 📝 Solution: 11 / 20 11. Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and product of its zeros as 3, −1 and −3 respectively. A) k [𝑥³ − 2𝑥² − 𝑥 − 3] B) k [𝑥³ − 3𝑥² − 𝑥 − 5] C) k [𝑥³ − 𝑥² − 𝑥 − 3] D) k [𝑥³ − 3𝑥² − 𝑥 − 3] 📝 Solution: 12 / 20 12. If 𝛼 and 𝛽 are the zeros of the quadratic polynomial f(x) = x² − 5x + 4, find the value of 1/𝛼 − 1/𝛽 − 2𝛼𝛽 A) 25/5 B) 22/3 C) -27/4 D) -22/7 📝 Solution: 13 / 20 13. If 𝛼 and 𝛽 are the zeros of the quadratic polynomial p(x) = 4x² − 5x −1, find the value of 𝛼²𝛽 + 𝛼𝛽² A) -5/7 B) -5/16 C) 5/8 D) 3/7 📝 Solution: Since 𝛼 𝑎𝑛𝑑 𝛽 are the roots of the polynomial: 4𝑥² − 5𝑥 − 1 14 / 20 14. Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and their co efficient [Type Your Answer Blow] : f(x) = 𝑥² − 2𝑥 − 8 A) -2, 4 B) -3, 4 C) -2, 3 D) 2, -4 📝 Solution: 15 / 20 15. If 𝛼 and 𝛽 are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate: 𝛼 − 𝛽 A) −4𝑎𝑐/2𝑎 B) 𝑏²−4𝑎𝑐/2𝑎 C) 2ab D) √𝑏²−4𝑎𝑐/2𝑎 📝 Solution: 16 / 20 16. If 𝛼 and 𝛽 are the zeros of a quadratic polynomial such that a + 13 = 24 and a − 𝛽 = 8, find a quadratic polynomial having 𝛼 and 𝛽 as its zeros. A) 𝑘[𝑥² − 2𝑥 + 120] B) 𝑘[𝑥² − 24𝑥 + 128] C) 𝑘[𝑥² − 24𝑥 + 125] D) 𝑘[𝑥² − 24𝑥 + 108] 📝 Solution: 17 / 20 17. If the zeroes of the polynomial 𝑓(𝑥) = 𝑥³ − 12𝑥² + 39𝑥 + 𝑘 are in A.P., find the value of k. A) 21 B) 25 C) -28 D) -24 📝 Solution: 18 / 20 18. Obtain all zeros of the polynomial 𝑓(𝑥) = 𝑥⁴ − 3𝑥² = 𝑥² + 9𝑥 − 6 if two of its zeros are −√3, 𝑎𝑛𝑑 √3. A) −√3, √2, 1, 0 B) −√3, √3, 1, 2 C) 2, 1, 0, -2 D) −√5, √2, 1, 0 📝 Solution: 19 / 20 19. If a and are the zeros of the quadratic polynomial f(x) = 𝑥² − 𝑥 − 4, find the value of 1/𝛼+1/𝛽− 𝛼𝛽 A) 15/4 B) 15/3 C) 12/3 D) 12/5 📝 Solution: 20 / 20 20. Obtain all zeros of f(x) = x3 + 13×2 + 32x + 20, if one of its zeros is −2. A) -1, -10, -2 B) -1, -10, -3 C) -1, -0, -2 D) -1, -5, -3 📝 Solution: Your score isShare Your Score with Friends Facebook Twitter 0% Send feedback
