# 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.

**Problem 21:**

Compute the sum of all the roots of (x-2)(x+1)+(x-1)(x+4)=0

**Solution:**

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**.

**Problem 22:**

If r and s are the roots of , evaluate

**Solution:**

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.

**Problem 23:**

For what value(s) of m are the roots of equal?

**Solution:**

For a quadratic equation to have an equal roots, the discriminant must be equal to 0. Thus,

**Problem 24:**

It is known that y varies as the square of x and y=8 when x=1. What is y when x=8?

**Solution:**

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,

**Problem 25:**

Suppose that x and y are inversely proportional and are positive quantities. By what percent does y decrease if x is increased by 25%?

**Solution:**

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%**.

### Dan

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