If x² + px + q = 0 , and x² + qx + p = 0 , ( p ≠ q ) , have a common root , show that , 1 + p + q = 0 , Also show that , their roots are the roots of the equation x² + x + pq = 0
Answers
Answered by
8
★ QUADRATIC RESOLUTION ★
Given function :
x² + px + q = 0
x² + qx + p = 0
By applying mathematical generality ,
x = 1 appears to be one of the roots , from which both equations we get 1 + p + q = 0 ,
From 1st equation : product of roots = q
Hence , roots of 1st equation : x = 1 and x = q
Similarly for 2nd equation :
x = 1 and x = p
The equations having roots p and q is -
x² - ( p + q ) x + pq = 0
Substituting the above results -
x² + x + pq = 0 [ 1 + p + q = 0 ]
★✩★✩★✩★✩★✩★✩★✩★✩★✩★✩★
Given function :
x² + px + q = 0
x² + qx + p = 0
By applying mathematical generality ,
x = 1 appears to be one of the roots , from which both equations we get 1 + p + q = 0 ,
From 1st equation : product of roots = q
Hence , roots of 1st equation : x = 1 and x = q
Similarly for 2nd equation :
x = 1 and x = p
The equations having roots p and q is -
x² - ( p + q ) x + pq = 0
Substituting the above results -
x² + x + pq = 0 [ 1 + p + q = 0 ]
★✩★✩★✩★✩★✩★✩★✩★✩★✩★✩★
Similar questions