Question

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.
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Answer 1

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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.

Answer 2

Find the equation whose roots are ‑1, ‑6, 2, ‑3 if the roots of the equation x4‑8x3+7x2+36x‑36=0 are 1, ‑2, 3, 6. *