Question

2x^2-28x+98=a(x-b)^2

In the expression above, a > 1 and both a and b are constants. which of the following could be the value of b?

a. -7
b. 7
c. 14
d. 49

Answer 1

To find the possible value of b, we can compare the given equation with the standard form of a quadratic equation:

ax^2 + bx + c = 0

First, let's expand the right-hand side of the given equation:

a(x - b)^2 = a(x^2 - 2bx + b^2)

= ax^2 - 2abx + ab^2

Comparing the expanded form with the given equation 2x^2 - 28x + 98 = a(x - b)^2, we can see that:

a = 2

-2ab = -28

Dividing both sides of the second equation by -2 gives:

ab = 14

Now, let's analyze the possible values of b based on the given options:

a. b = -7

Since a > 1, it cannot be negative.

b. b = 7

This value satisfies the condition, as it gives ab = 2 7 = 14.

c. b = 14

This value also satisfies the condition, as it gives ab = 2 14 = 28.

d. b = 49

This value does not satisfy the condition, as it gives ab = 2 * 49 = 98, which is not equal to 14.

Therefore, the possible value of b is either 7 or 14.