Consider the quadratic function f(y) = 8y2 – 7y + 6. What is the constant of the function?

Given the quadratic function:

f(y) = 8y^2 - 7y + 6

a = 8

b = -7

c= 6

Find the zeros.

Solution:
In order to solve for the roots or zeros of an equation, we simply must look at the 2nd and 3rd value. First we must think of two numbers that when added, the answer is -7, and when multiplied, the answer is 6. Hence, if we are unable to find the number, we will use the quadratic formula.

The Quadratic formula:

y = −b ± √(b^2 − 4ac)/2a

is used to solve quadratic equations where a ≠ 0, in the form
ax^2+bx+c=0

When b^2−4ac=0 there is one real root.

When b^2−4ac>0 there are two real roots.

When b^2−4ac<0 there are no real roots, only a complex number.

Substitute the given values of a, b and c to the quadratic formula.

y = −b ± √(b^2 − 4ac)/2a

y = −(-7) ± √((-7)^2 − 4(8)(6))/2(8)

y = 7 ± √(49 − 288)/16

y = 7 ± √(-274)/16

Since we have a negative answer inside the square root sign, this means that the resulting number will be a complex number, or an imaginary number, hence we will not have any real solution for the given quadratic equation.

Final answer:
 

No Solution