Find P, if the roots of the equation #x^2+3x+p-2 = 0# differ by #2# ?

Question

1403 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-22T16:52:02

# 13/4#.

Let, #alpha and beta# be the roots of the given quadr. eqn.

Then, we know that,

#alpha+beta=-3/1=-3 and alpha*beta=(p-2)/1=(p-2)#.

Now, #(alpha-beta)^2=(alpha+beta)^2-4alpha*beta#.

#:. (alpha-beta)^2=(-3)^2-4(p-2)=17-4p#.

But, we are given that, #(alpha-beta)=+-2#.

#:. 17-4p=4, or, p=13/4#, as desired!