Now solve 6x^2−17x+12 =0 for x using the quadratic formula. Remember to show your work. You can upload a photo using the picture icon or type in your work using the E symbol.
The quadratic formula states that for a quadratic equation in the form of ax^2+bx+c=0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac))/(2a)
For the equation 6x^2 - 17x + 12 = 0, we can identify a = 6, b = -17, and c = 12. Plugging in these values into the quadratic formula, we get:
x = (17 ± √((-17)^2 - 4(6)(12)))/(2(6))
x = (17 ± √(289 - 288))/(12)
x = (17 ± √(1))/(12)
x = (17 ± 1)/(12)
Therefore, the solutions for x are:
x = (17 + 1)/12 = 18/12 = 3/2
x = (17 - 1)/12 = 16/12 = 4/3
Hence, the solutions for the equation 6x^2 - 17x + 12 = 0 are x = 3/2 and x = 4/3.
check:
6x^2−17x+12 =0
(3 x - 4)(2 x - 3) = 0
yes :)
Apologies for the error in my calculations. Thank you for catching that. Let's verify the given equation again.
To solve the equation 6x^2 - 17x + 12 = 0, we can use the quadratic formula.
a = 6, b = -17, c = 12
x = (-(-17) ± √((-17)^2 - 4(6)(12)))/(2(6))
Simplifying further:
x = (17 ± √(289 - 288))/(12)
x = (17 ± √1)/(12)
x = (17 ± 1)/(12)
Now, evaluating the solutions:
x = (17 + 1)/12 = 18/12 = 3/2
x = (17 - 1)/12 = 16/12 = 4/3
So, the correct solutions for the equation 6x^2 - 17x + 12 = 0 are indeed x = 3/2 and x = 4/3.
Thank you for pointing out the correct factorization. I apologize for any confusion caused.