Sir,

For 2 Quadratic Equations what is the difference between the conditions when both have one and only one root in common and when both have atleast one root in common?Could you explain with suitable example and illustration?

Question

Sir,

For 2 Quadratic Equations what is the difference between the conditions when both have one and only one root in common and when both have atleast one root in common?Could you explain with suitable example and illustration?

Askiitian.Expert Rajat · Answer

If we take two quadtratic equations: ax 2 + bx + c = 0 and mx 2 + nx + p = 0 Case I : Only One Common root In this case Let that common root be &yen; Then a&yen; 2 + b&yen; + c = 0 and m&yen; 2 + n&yen; + p = 0 Now add the two equations to get another quadratic equation: (a+m)&yen; 2 + (b+n)&yen; + c+p = 0 Replace &yen; by x (a+m)x 2 + (b+n)x + c+p = 0. Now this quadratic has only ine root That means D = 0 Or, (b+n) 2 -4(a+m)(c+p) = 0 Case II : Atleast One common root: Here D of [(a+m)x 2 + (b+n)x + c+p = 0. ] D>=0 or (b+n) 2 -4(a+m)(c+p) >=0

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Sir, For 2 Quadratic Equations what is the difference between the conditions when both have one and only one root in common and when both have atleast one root in common?Could you explain with suitable example and illustration?

Sir,

For 2 Quadratic Equations what is the difference between the conditions when both have one and only one root in common and when both have atleast one root in common?Could you explain with suitable example and illustration?

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Sir, For 2 Quadratic Equations what is the difference between the conditions when both have one and only one root in common and when both have atleast one root in common?Could you explain with suitable example and illustration?

Sir, For 2 Quadratic Equations what is the difference between the conditions when both have one and only one root in common and when both have atleast one root in common?Could you explain with suitable example and illustration?

1 Answers

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Sir,

For 2 Quadratic Equations what is the difference between the conditions when both have one and only one root in common and when both have atleast one root in common?Could you explain with suitable example and illustration?