Q Find the value(s) of 'p' for which the equation ax2-px+ab=0 and x2-ax-bx+ab=0 may have a common root, given - Maths - Complex Numbers and Quadratic Equations

Question

Q Find the value(s) of 'p' for which the equation a x 2 -px+ab=0
and x 2 -ax-bx+ab=0 may have a common root, given a,b are non zero
real numbers?

Lovina Kansal · Accepted Answer

Dear student
We have,x2-ax-bx+ab=0⇒x2-(a+b)x+ab=0⇒x2-bx-ax+ab=0⇒x-ax-b=0⇒x-a=0 or x-b=0⇒x=a or x=bIf x=a is the root of the other equation,a3-pa+ab=0⇒p=a2+bIf x=b is the root of the other equation,ab2-pb+ab=0⇒p=a(1+b)Hence p=a2+b or a(1+b)
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Q. Find the value(s) of 'p' for which the equation a x 2 -px+ab=0 and x 2 -ax-bx+ab=0 may have a common root, given a,b are non zero real numbers?

Q. Find the value(s) of 'p' for which the equation a $x^{2}$ -px+ab=0 and $x^{2}$ -ax-bx+ab=0 may have a common root, given a,b are non zero real numbers?