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If α and β are zeroes of polynomial 2x²-4x+5.Then find the value of following:(a) α²+β²(b) 1/α+1/βPlease answer fast ...... |
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Answer» Answer: a) -1 B) 4/5 Step-by-step EXPLANATION: α and β are zeroes of polynomial 2x²-4x+5. So equate the polynomial to 0. 2x^2 - 4x +5=0 Sum of roots = -(coefficient of x)/coefficient of x^2 = α+β Product of roots = (constant)/coefficient of x^2 = αβ Sum of roots=α+β=4/2=2 Product of roots = αβ = 5/2 We need to find α²+β² which can be written as - α²+β²=(α+β)²-2αβ Now put values of αβ and α+β in above equation α²+β²=(2)² - 2(5/2) = 4 - 5 = -1 1/α+1/β can be written as 1/α+1/β=(α+β)/αβ -----------[ By taking LCM as αβ ] Now we know values of α+β and αβ , so by USING those values in above equation we get - 1/α+1/β=2/(5/2) = 4/5 |
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