What is the solution using the quadratic formula to solve x^2-3x+9/4=0

Question

What's the answer

Answer 1

It would be easier to just factor since this polynomial is a perfect square, but since your teacher is asking you to use the quadratic formula, we'd better do that too:

You have:

y = ax2 + bx + c

y = x^2 - 3x + 9/4

a = 1, b = -3, c = 9/4

The quadratic formula gives you the values of x when y = 0:

x = (-b + or - square root (b^2-4ac)) / 2a

x = (3 + or - square root (9 - 9)) / 2

x = (3 + sqrt(0) )/ 2 ; (3 - sqrt(0) )/ 2

x = 3/2

 

You can use factoring or completing the square to check your answer, or graph it on your calculator to double check your answer.

Hope this helps!

Answer 2

Hello Ty, 

you will need both the binomial formula here and the "complete the square" step to transform your equation. The expression on the left happens to be a perfect binomial already and you can transform it to its basic expression being (x-3/2)^2.
Now the only way that this expression is ever zero, is when the value in brackets is zero. Which is only true when x=3/2. Then you'll have (3/2 - 3/2)^2 = 0 or 0^2=0

Answer 3

This is a perfect square.

(x - 3/2)^2 = 0

Answer: x = 3/2