Question

If the root of both the equation 2 + 2 + = 0 and 2 − 2 + = 0 are real then prove that 2 =

Answer 1

Answer:

Equation px

2

+2qx+r=0 and qx

2

−2

pr

x+q=0 have real roots, then

b

2

−4ac≥0 for both equations

From first

4q

2

−4pr≥0⇒q

2

≥pr ...............(1)

and from second

4(pr)−4q

2

≥0 (for real root)

⇒pr≥q

2

...............(2)

From (1) and (2), we get result q

2

=pr