Question 8:
What is the value of c such that: x2 + 14x + c, is a perfect-square trinomial?
a. 7
b. 98
c. 196
d. 49
so, even though Bosnian started out with a yes his work shows that the answer was D, not A.
The answer is 49
Yes.
( x + c ) ^ 2 = x ^ 2 + 2 * x * c + c ^ 2
In this case :
2 x c = 14 x Divide both sides bny 2 x
2 x c / 2 x = 14 x / 2 x
c = 7
So :
( x + c ) ^ 2 = x ^ 2 + 2 * x * c + c ^ 2
( x + 7 ) ^ 2 = x ^ 2 + 2 x * 7 + 7 ^ 2 =
x ^ 2 + 14 x + 49
To find the value of c such that the trinomial x^2 + 14x + c is a perfect square, we need to understand what makes a trinomial a perfect square.
A perfect square trinomial has the form (x + a)^2, where a is a constant. When expanded, (x + a)^2 simplifies to x^2 + 2ax + a^2.
Comparing this form to the given trinomial, we can see that the coefficient of x^2 in both expressions is 1, so a = 1.
Now, let's expand (x + 1)^2: (x + 1)(x + 1) = x^2 + x + x + 1 = x^2 + 2x + 1.
Comparing the expanded form and the given trinomial, we can see that c = 1.
Therefore, the value of c that makes x^2 + 14x + c a perfect square trinomial is 1.
None of the answer choices provided (a. 7, b. 98, c. 196, d. 49) are equal to 1, so none of them are correct.