Q) If X = and X = − 3 are the roots of the equation aX² + 7X + b = 0, find the values of a and b.

Ans: We know that if a and b are the roots of a polynomial, then the polynomial can be given by (X – a) (X – b) = 0

Here, we are given that X = and X = −3 are roots of the equation aX² + 7X + b = 0

∴  (X − ) (X − (−3)) = 0

∴  X² − X + 3 X – ()(3) = 0

∴  X² + X (3 – ) – 2 = 0

∴  X² + X () – 2 = 0

∴  3 X² + 7 X – 6 = 0

∴  3 X² + 7 X – 6 = aX² + 7X + b

By comparing LHS & RHS, we get:

3 = a or a = 3

and – 6 = b or b = − 6

Therefore, values are a = 3 and b = – 6.

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