Question

if the quadratic equations 3x²+ax+1=0 and 2x²+bc+1=0 have comman real root ,then the value of the expression 5ab-2a²-3b²=0
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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