find the number of zeros(x-intercept) y=a^2+a-56 show the step please.
Factor
What factors multiply to equal 56 and subtract to
equal 1?
-7.8
Yes
(X-7)(x+8)
Check by foiling
X^2 +8x -7x -56
X^2 +x -56
To find the x-intercepts of the equation y = a^2 + a - 56, you need to find the values of 'a' for which y equals zero. In other words, you need to solve the equation a^2 + a - 56 = 0. Here are the steps to do that:
Step 1: Write the equation: a^2 + a - 56 = 0.
Step 2: Factorize the equation if possible. In this case, you need to find two numbers whose sum is 1 and whose product is -56. Since there are no such numbers, you cannot factorize the equation.
Step 3: Use the quadratic formula. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b^2 - 4ac)) / (2a).
In our case, a = 1, b = 1, and c = -56. Substituting these values into the quadratic formula yields:
a = 1, b = 1, c = -56.
x = (-1 ± √(1^2 - 4(1)(-56))) / (2(1)).
Simplifying further:
x = (-1 ± √(1 + 224)) / 2.
x = (-1 ± √225) / 2.
x = (-1 ± 15) / 2.
This gives us two possible values for x:
x = (-1 + 15) / 2 = 14 / 2 = 7.
x = (-1 - 15) / 2 = -16 / 2 = -8.
So, the equation y = a^2 + a - 56 has two x-intercepts: x = 7 and x = -8.