2)
1 answer:
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Answer:
The correct option is C). (9,4)
The coordinates of a point N is (9,4)
Step-by-step explanation:
Theory: If point P(x,y) lies on line segment AB and AP: PB=m:n, then we say P divides line AB internally in ratio of m:n and Point is given by
P=
Given that point, M is lying somewhere between point L and point N.
The coordinates of a point L is (-6,14)
The coordinates of a point M is (-3,12)
Also, LM: MN = 1:4
We can write as,
Let,
Point L(-6,14)=(X1, Y1)
Point M(-3,12)=(x,y)
Point N is (X2, Y2)
m=1 and n=4
M(-3,12)=
M(-3,12)=
M(-3,12)=
(-15)=X2-24
X2=9
(60)=Y2+56
Y2=4
Thus,
The coordinates of a point N is (9,4)
Result: The correct option is C). (9,4)
Answer:
k = - , k = 2
Step-by-step explanation:
Using the discriminant Δ = b² - 4ac
The condition for equal roots is b² - 4ac = 0
Given
kx² + 2x + k = - kx ( add kx to both sides )
kx² + 2x + kx + k = 0 , that is
kx² + (2 + k)x + k = 0 ← in standard form
with a = k, b = 2 + k and c = k , thus
(2 + k)² - 4k² = 0 ← expand and simplify left side
4 + 4k + k² - 4k² = 0
- 3k² + 4k + 4 = 0 ( multiply through by - 1 )
3k² - 4k - 4 = 0 ← in standard form
(3k + 2)(k - 2) = 0 ← in factored form
Equate each factor to zero and solve for k
3k + 2 = 0 ⇒ 3k = - 2 ⇒ k = -
k - 2 = 0 ⇒ k = 2