How you you work out this question?

k<0 or k>4

Step-by-step explanation:

In the generic equation ax² + bx + c = 0, there are two solutions only if discriminant D>0 where D = b²-4ac.

Mapping your equation on the generic means that:

a = k

b = k

c = 1

So when we have to solve D>0 we solve:

k² - 4k > 0

k(k-4) > 0

roots are k=0 and k=4

k² - 4k > 0 when k<0 or k>4

k < 0 or k > 4

Step-by-step explanation:

kx² + kx + 1 = 0

Two solutions:

b²-4ac > 0

(k)²-4(k)(1) > 0

k² - 4k > 0

k(k-4) > 0

k < 0 or k > 4

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12

x = -4

step-by-step explanation:

- 20 - 4(x + 3) = 4x

=> -20 - 4x - 12 = 4x

=> - 32 -4x = 4x

=> -32 = 4x + 4x

=> - 32 = 8x

=> -32/8 = x

=> -4 = x