Question

Solve the quadratic equation 2x^2 - 7x + 11 = 0 using the quadratic formula.

a) x = –0.8, x = –5.8
b) x = 4.6, x = 2.4
c) x = 2.2, x = –0.2
d) x = 1.75 + 1.56i, x = 1.75 – 1.56i

Answer 1

The quadratic equation 2x^2 - 7x + 11 = 0 is solved using the quadratic formula, yielding complex solutions since the discriminant is negative. The solutions are x = 1.75 + 1.56i and x = 1.75 - 1.56i.

Step-by-step explanation:

To solve the quadratic equation 2x^2 - 7x + 11 = 0 using the quadratic formula, you first identify the coefficients a, b, and c from the equation, which are a=2, b=-7, and c=11 respectively. The quadratic formula is:

x = −b ± √(b2 − 4ac)
2a

Plugging in the values:

x = −(−7) ± √((−7)2 − 4(2)(11))
2(2)

x = 7 ± √(49 − 88)
4

x = 7 ± √(−39)
4

Since the discriminant (49 − 88) is negative, this means the solutions will be complex numbers. The solutions are:

x = 7 ± 3.162i
4

x = 1.75 ± 1.56i

Therefore, the solutions to the quadratic equation are x = 1.75 + 1.56i and x = 1.75 – 1.56i.