Question

If the root of x2 + px + 12 = 0 are in the ratio 1:3 then the value of P is​

Answer 1

Answer:

x^2 + px + 12 = 0

The two roots are: x1 = [-p +(p^2 - 48)^0.5]/2

x2 = [-p -(p^2 - 48)^0.5]/2

Now x1:x2::3:1, or

[-p +(p^2 - 48)^0.5]/2 : [-p -(p^2 - 48)^0.5]/2 :: 3:1 or

[-p +(p^2 - 48)^0.5]/2 =3*[-p -(p^2 - 48)^0.5]/2, or

[-p +(p^2 - 48)^0.5] =3*[-p -(p^2 - 48)^0.5], or

-p + 3p = -3*(p^2 - 48)^0.5 -(p^2 - 48)^0.5, or

2p = -4*(p^2 - 48)^0.5

Squaring both sides we get

4p^2 = 16(p^2 - 48), or

p^2 = 4(p^2 - 48), or

p^2 = 4p^2 - 192, or

3p^2 = 192, or

p^2 = 192/3 = 64, or

p = 8.

Check: x^2 + 8x + 12 = 0

This can be factorized as (x+2)(x+6) = 0

Hence x = -2 or -6. One factor is three times the other.

Step-by-step explanation: