if x=2|3and x=-3are roots of the quadratic equation ax2+1x+b=0find the values of a and b
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Step-by-step explanation:
Given, x=2|3and x=-3 are roots of the quadratic equation ax2+1x+b=0
If x = 2/3 , then a(2/3)² + 1(2/3) + b = 0
=> 4a/9 + 2/3 + b = 0 => (4a + 6 + 9b) / 9 = 0
=> 4a + 6 + 9b = 0 => 4a + 9b = -6 ---------(1)
If x = -3 , then a(-3)² + 1(-3) + b = 0
=> 9a - 3 + b = 0 => b = 3 - 9a ---------(2)
from (1) & (2)
4a + 9(3-9a) = -6 => 4a + 27 - 81a= -6
=> 4a - 81a= -6 - 27
=> - 77a = -33
=> a = -33 / -77 = 3 / 7
substituting in eq (2)
b = 3 - 9(3/7) = 3 - 27/7 = (21-27) / 7
=> b = -6 / 7
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