find the value Of k of the product pf the roots of 2x square - 6x + k = 0 is 4.
The product of the roots of a polynomial in the form,ax^2+bx+c=0,can be taken as (c/a)
so in this case (k/2)=4
k=8
A motorist Drove 100km. if he had gone 5 km per hour faster he could
made his trip 1 hour less time. how fast did he drive?
You can do this one by inspection, since you know that
5*20 = 4*25 = 100
Still, to solve this kind of problem in general, follow the steps. Write what they tell you, then work for a solution:
vt = 100
(v+5)(t-1) = 100
(v+5)(100/v-1) = 100
(v+5)(100-v) = 100v
v^2+5v-500 = 0
(v-20)(v+25) = 0
v = 20
To find the value of k in the equation 2x^2 - 6x + k = 0 when the product of its roots is 4, we can use the fact that the product of the roots of a quadratic equation ax^2 + bx + c = 0 is given by c/a.
In this case, the quadratic equation is 2x^2 - 6x + k = 0, so we need to find the value of k such that the product of the roots is 4.
First, let's find the roots of the equation by using the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
In this case, a = 2, b = -6, and c = k. Substituting these values into the quadratic formula, we have:
x = (-(-6) ± sqrt((-6)^2 - 4(2)(k))) / (2(2))
x = (6 ± sqrt(36 - 8k)) / 4
x = (6 ± sqrt(36 - 8k)) / 4
Now, we can find the product of the roots:
Product of the roots = [(6 + sqrt(36 - 8k)) / 4] * [(6 - sqrt(36 - 8k)) / 4]
= (36 - (36 - 8k)) / 16
= (8k) / 16
= k / 2
We know that the product of the roots is 4, so we can set k/2 equal to 4:
k / 2 = 4
Now, we can solve this equation for k:
k = 4 * 2
k = 8
Therefore, the value of k in the equation 2x^2 - 6x + k = 0 when the product of its roots is 4 is 8.