Question

HELP ASAP PLEASE!!!

Use the quadratic formula to solve: 2ײ-7×-21=0

Round your answer to two decimal places.

1
-5.43 and 1.93

2
-1.93 and 5.43

3
-4.5 and 0.98

4
no real solution

Answer 1

The quadratic fomula:

`ax^2+bx+c=0\\\\\Delta=b^2-4ac\\\\If\ \Delta<0,\ then\ \boxed{NO\ SOLUTION}\\\\If\ \Delta=0,\ then\ \boxed{ONE\ SOLUTION:\ x=(-b)/(2a)}\\\\If\ \Delta>0,\ then\ \boxed{TWO\ SOLUTIONS:\ x_1=(-b-\sqrt\Delta)/(2a)\ and\ x_2=(-b+\sqrt\Delta)/(2a)}-----------------------------------------------`

We have the equation:

`2x^2-7x-21=0\\\\a=2,\ b=-7,\ c=-21\\\\\Delta=(-7)^2-4(2)(-21)=49+168=217 > 0\\\\x_1=(-(-7)-√(217))/(2(2))=(7-√(217))/(4)\approx-1.93\\\\x_2=(-(-7)+√(217))/((2)(2))=(7+√(217))/(4)\approx5.43\\\\Answer:\ \boxed{\boxed{2.\ -1.93\ and\ 5.43}}`