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5. If x = 2/3 and x = -3 are the roots of the equation ax? + 7x + b = 0, find the values of a and b.​

Answer»

EXPLANATION.x = 2/3  and  x = -3 are the roots of the equation,⇒ ax² + 7X + b = 0.As we know that,Put the value of x = 2/3 in equation, we get.⇒ a(2/3)² + 7(2/3) + b = 0.⇒ a(4/9) + 14/3 + b = 0.⇒ 4a/9 + 14/3 + b = 0.Taking L.C.M in equation, we get.⇒ 4a + 42 + 9B = 0. ⇒ (1).Put the value of x = -3 in equation, we get.⇒ a(-3)² + 7(-3) + b = 0.⇒ a(9) - 21 + b = 0.⇒ 9a - 21 + b = 0.⇒ b = 21 - 9a ⇒ (2).Put the value of equation (2) in equation (1), we get.⇒ 4a + 42 + 9(21 - 9a) = 0.⇒ 4a + 42 + 189 - 81a = 0.⇒ 231 - 77a = 0.⇒ 77a = 231.⇒ a = 3.Put the value of a = 3 in equation (2), we get.⇒ b = 21 - 9(3).⇒ b = 21 - 27.⇒ b = -6.Values of A = 3 & B = -6.


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