Use the quadratic formula to solve the quadratic equation 2x2−9x+11=0
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Express its solutions in the form a±bi
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(1 point)
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac))/(2a)
For the equation 2x^2 - 9x + 11 = 0, we can identify a = 2, b = -9, and c = 11.
Plugging these values into the quadratic formula, we get:
x = (-(-9) ± √((-9)^2 - 4(2)(11)))/(2(2))
= (9 ± √(81 - 88))/(4)
= (9 ± √(-7))/(4)
Since the expression under the square root (√(-7)) is negative, we can rewrite it in the form of a complex number by introducing the imaginary unit, i:
x = (9 ± √(-1 * 7))/(4)
= (9 ± i√7)/(4)
Therefore, the solutions to the quadratic equation 2x^2 - 9x + 11 = 0 are:
x = (9 + i√7)/(4) and x = (9 - i√7)/(4)