For example, the additive inverse of 12 is –12. The additive inverse of –3 is 3. Formally, the additive inverse of x is –x. Note: The sum of a number and its additive inverse is 0.
Answer: The value of a is 1. The value of b is -1. The value of c is 1. The value of the discriminant is -3. The quadratic function will not intersects the x-axis.
Explanation:
The standard form of a quadratic equation is,
The given function is,
It can be written as,
By comparing this equation with the standard form of quadratic equation. we get,
The formula for discriminant is,
The value of the discriminant is -3.
If D<0, it means the function have no real roots.
If D=0, it means function have one real roots.
If D>0, it means function have two real roots.
Since D<0 it means the function have no real roots. So the function will not intersect the x-axis at any point.
Answer:
In the given figure the point on segment PQ is twice as from P as from Q is. What is the point? Ans is (2,1).
Step-by-step explanation:
There is really no need to use any quadratics or roots.
( Consider the same problem on the plain number line first. )
How do you find the number between 2 and 5 which is twice as far from 2 as from 5?
You take their difference, which is 3. Now splitting this distance by ratio 2:1 means the first distance is two thirds, the second is one third, so we get
4=2+23(5−2)
It works completely the same with geometric points (using vector operations), just linear interpolation: Call the result R, then
R=P+23(Q−P)
so in your case we get
R=(0,−1)+23(3,3)=(2,1)
Why does this work for 2D-distances as well, even if there seem to be roots involved? Because vector length behaves linearly after all! (meaning |t⋅a⃗ |=t|a⃗ | for any positive scalar t)
Edit: We'll try to divide a distance s into parts a and b such that a is twice as long as b. So it's a=2b and we get
s=a+b=2b+b=3b
⇔b=13s⇒a=23s
I would change the 1 2/5 miles to a whole fraction which would be 7/5 miles then invert the 5/8 th to 8/5 then multiply the fractions. I.E. 7/5 x 8/5 which will give 56/25. Divide 25 into 56 and you get 2 6/25 miles or convert to a decimal and would be 2.24 miles.
