Is the Sequence 4x ^ 2 – 5x – 12 equal to 0?

No, the equation 4x^2 – 5x – 12 is not equal to 0.

To determine whether the equation 4x²– 5x – 12 equals 0, we need to solve it for x and check if there are any real solutions.

To solve this quadratic equation, we can use the quadratic formula:

x = – b ± √(b−4ac) ÷ 2a​​

In this equation, a = 4, b = -5, and c = -12. Plugging these values into the quadratic formula:

x= −(−5)±(−5)²−4(4)(−12)​​ ÷ 2(4)

Simplify:

x = 85 ± 25+192​​

x = 85 ± 217​​

Now, we check if there are real solutions. The term inside the square root, 217, is positive, so there are two real solutions for x:

x = 85 + 217​​ and x = 85 − 217​​

So, the equation 4x²– 5x – 12 does have real solutions, and these are the values of x that make it equal to 0.