Equations with Common Roots (1 Viewer)

[xwrathbringerx]

1. Show that, if the equations x^2 + 2px + q = 0 and x^2+2Px+Q=0 have a common root, then (q-Q)^2+4(P-p)(Pq-pQ)=0.

2. Find the conditions that the equations x^2+2x+a=0 and x^2+bx+3 should have a common root.

 

[Timothy.Siu]

1. Show that, if the equations x^2 + 2px + q = 0 and x^2+2Px+Q=0 have a common root, then (q-Q)^2+4(P-p)(Pq-pQ)=0.

2. Find the conditions that the equations x^2+2x+a=0 and x^2+bx+3 should have a common root.

i think for the first one, just use the quadratic formula on one of them, and sub that into the other equation, and simplify, and you should get what you need to show.

The second question, just use the first part

 

[Trebla]

 

[xwrathbringerx]

Is the 2nd question really (a-3)^2 + 4(b-2)(ab-6) = 0?