Question

if one root of equation x2+12x-k=0. if one root of equation is thricethe other. then find the value of k.

Answer 1

Given equation = x^2 +12x -K
Also given = one root is thrice the other
Let one root be =α
Other root=β
3β=α
As this is a quadratic equation thus the sum of roots will be
α+β= -b/a
α+ 3α= -12/1
4α= -12
α= -3
Thus one root is -3
Putting the value of -3 in the polynomial
x^2 +12x -K
(-3)^2 +12(-3) -K=0
9 -36 -K=0
-27 -K=0
K=27

Answer 2

Answer:

x^2+12x-k=0

Let one root be α

And other root isβ

3=α/β

3β=α

So,

α+β= -b/a

α+ 3α= -12/1

4α= -12

α= -3

Putting the value in eq

(-3)^2+12(-3)-k=0

9-36-k=0

-27-k=0

-k=27

k=-27

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