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2x 2 +mxy+3y 2 -5y-2 have two rational factors find 'm'?

2x2+mxy+3y2-5y-2 have two rational factors find 'm'?

Grade:11

1 Answers

Y RAJYALAKSHMI
45 Points
9 years ago
Consider this as an equation only in ‘x’.  This has a rational roots only when b^2 – 4ac = 0 or a perfect square.
=> (my^2 – 4 * (3y^2 – 5y – 2) * 2 = y^2(m^2 – 24) + 40y + 16 is a perfect square or ‘0’
=> m^2 – 24 = 25 or 49
but the condition is satisfied only when m^2 = 49 
=> m = +7 or -7.
 
 

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