2015 MTAP Reviewer for Grade 9 Solutions(21-25)
This is already the 5th part of the reviewer solution series for grade 9 MMC. You may check the previous parts in this section.
Compute the sum of all the roots of (x-2)(x+1)+(x-1)(x+4)=0
To find the sum of the roots, we expand the equation,
Now, the sum of the roots of this quadratic equation is just the negative ratio of b and a. Thus, the sum is -1.
If r and s are the roots of , evaluate
The sum of the roots of quadratic equation is again the negative ratio of b and a. Thus,
This means that .
Actually, this problem doesn’t really make sense at all. I was expecting a twist somewhere. They might mistyped this from this . The latter is more challenging and adds flavor to the problem. Anyways, let’s proceed.
For what value(s) of m are the roots of equal?
For a quadratic equation to have an equal roots, the discriminant must be equal to 0. Thus,
It is known that y varies as the square of x and y=8 when x=1. What is y when x=8?
Let k be the constant of proportionality. Since y varies as the square of x we have,
Solving for k when y=8 and x=1,
Solving for y when x=8,
Suppose that x and y are inversely proportional and are positive quantities. By what percent does y decrease if x is increased by 25%?
We let k be the constant of proportionality and we establish the equation.
IF x in increased by 25%, the value of x will become 1.25x. Since the constant of proportionality is constant. We equate the ks of two situations.
From 1, the value of y decreases to 0.8. Thus, it decreased by 20%.