need help with maths question (1 Viewer)

[wolf7]

need help with maths question(i add another question)

Find the value of m in

x^2+2mx-6 = 0 if one of the root is zero

can ya plz show the working out

Also

another question
]
Find the qudratic equation whose roots are

3 - √2 and 3 + √2

also

For what value of k will the equation x^2 - (k+2)x+(k-4) = have :

(a) one root equal to 4
(b) one root which is the reciprocal of the other?

 

[rama_v]

let the roots be @ and 0

@ + 0 = -b/a = -2m
@0 = 0

Therefore @ = -2m
so the equation of the quaratic is (x+2m)(x-0) = 0

(x+2m)(x) = 0
x = -2m
m = x/-2

2nd question
3 - sqrt2
3 + sqrt2
so the equation is just (x-(3-sqrt2))(x-(3 + sqrt2)) ... just expand it out and you get the answer

 

[Slidey]

I suggest you learn these two formulae:
for ax^2+bx+c, where u,v are roots:
u+v=-b/a
uv=c/a

This will help tremendously in the future when you get this type of question.

Now:

"Find the qudratic equation whose roots are

3 - √2 and 3 + √2"

Different solution:
u+v=6
uv=3^2-2=7
.'. x^2-6x+7

Next:

"For what value of k will the equation x^2 - (k+2)x+(k-4) = have :

(a) one root equal to 4
(b) one root which is the reciprocal of the other?"

a)
u+v=u+4=k+2 -> u+2=k
uv=4u=k-4 -> 4u=u-2 -> u=-2/3, so k=4/3
b) Only consider the product of the roots: uv:
uv=u*1/u=1=k-4
.'. k=5

For the first question: Huh?

For a root to be zero, the equation must be of the form: ax^2+bx. No constant!