17. Find $$ c $$ so that the expression is a perfect square trinomial. a) $$ \quad x^{2}+6 x+c $$ b) $$ \quad x^{2}-20 x+c $$ c) $$ \quad x^{2}+x+c $$

Question

UpStudy AI · Accepted Answer

We start with the fact that a quadratic $$ x^2 + bx + c $$ is a perfect square trinomial if it can be written in the form

$$
(x + a)^2 = x^2 + 2ax + a^2.
$$

This means we need

$$
2a = b \quad \text{and} \quad a^2 = c.
$$

Thus, given any $$ b $$, we find

$$
a = \frac{b}{2} \quad \text{and} \quad c = \left(\frac{b}{2}\right)^2.
$$

### a) $$ x^2 + 6x + c $$

Here, $$ b = 6 $$. Then

$$
a = \frac{6}{2} = 3 \quad \text{and} \quad c = 3^2 = 9.
$$

### b) $$ x^2 - 20x + c $$

In this case, $$ b = -20 $$. Then

$$
a = \frac{-20}{2} = -10 \quad \text{and} \quad c = (-10)^2 = 100.
$$

### c) $$ x^2 + x + c $$

Now, $$ b = 1 $$. Then

$$
a = \frac{1}{2} \quad \text{and} \quad c = \left(\frac{1}{2}\right)^2 = \frac{1}{4}.
$$
To make each expression a perfect square trinomial, the value of $$ c $$ should be: a) $$ c = 9 $$ b) $$ c = 100 $$ c) $$ c = \frac{1}{4} $$

Find so that the expression is a perfect square trinomial.
a)
b)
c)

Upstudy AI Solution

Answer

Solution

Beyond the Answer

Related Questions

Latest Algebra Questions

Find so that the expression is a perfect square trinomial. a) b) c)