Question

if the quadratic equations 3x^2+ax+1=0 and 2x^2+bx+1=0 have a common root then the value of the expression 5ab-2a^2-3b^2 is​

Answer 1

Answer:

3x2 + ax + 1 = 0, 2x2 + bx + 1 = 0 have a common root.

Subtracting these equations, we get x2 + (a − b)x = 0

⇒ x = 0,

x = (b − a)

Clearly the common root is (b − a),

So 3(b − a) 2 + a(b − a) + 1 = 0

⇒ 3b2 + 3a2 − 6ab + ab − a2 + 1 = 0

⇒5ab − 2a2 − 3b2 = 1

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