Use the quadratic formula to solve the equation. Give exact answers.
2x^2 + 11x - 21 = 0
a) -3/2, 7
b) 3/2, -7
c) 3/2, 7
d) -3/2, -7
I could not get any of these answers.
The answer is (b), x1=3/2, x2=-7
Check that you use the formula
x=(-b+/-sqrt(B2-4ac))/(2a)
To use the quadratic formula, we have to identify the coefficients of the quadratic equation. In this case:
a = 2
b = 11
c = -21
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac))/(2a)
Substituting our coefficients into the formula, we get:
x = (-(11) ± √((11)^2 - 4(2)(-21)))/(2(2))
Simplifying further:
x = (-11 ± √(121 + 168))/4
x = (-11 ± √(289))/4
x = (-11 ± 17)/4
This gives us two possible solutions:
x₁ = (-11 + 17)/4 = 6/4 = 3/2
x₂ = (-11 - 17)/4 = -28/4 = -7
So, the correct answer is option c) 3/2, 7.