Use the quadratic formula to solve the equation:
\[ 9x^2 - 6x - 11 = 0 \]
Where the quadratic formula is given by:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
Answer (2)
9 x 2 − 6 x − 11 = 0 a = 9 , b = − 6 , c = − 11 Δ = b 2 − 4 a c = ( − 6 ) 2 − 4 ∗ 9 ∗ ( − 11 ) = 36 + 396 = 432 Δ = 432 = 144 ∗ 3 = 12 3 x 1 = 2 a − b − Δ = 2 ∗ 9 6 − 12 3 = 18 6 ( 2 − 2 3 ) = 3 2 − 2 3 x 2 = 2 a − b + Δ = 2 ∗ 9 6 + 12 3 = 18 6 ( 2 + 2 3 ) = 3 2 + 2 3
To solve the quadratic equation 9 x 2 − 6 x − 11 = 0 , we used the quadratic formula and found the discriminant to be 432 . This led to the solutions x 1 = 3 2 − 2 3 and x 2 = 3 2 + 2 3 .
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