5. If x = 2/3 and x = -3 are the roots of the equation ax^2 + 7x + b = 0, find the values of
and b.
Answers
Answer:
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Step-by-step explanation:
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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.