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Use the quadratic formula to find the roots of the equation. x^2 + 3x - 18 = 0 A. {-6, 3} B. {-2, 9} C. {-3, 6} D. {-9, 2}
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=(x-3)(x+6) x_1=3 x_2=-6
A. is right
x^2 + 3x - 18 = -3 +/- the square root of ((3)^2 - (-18)(4)(1) all over 2(1)) = -3 +/- the square root of (9 + 72) all over 2 = -3 +/- the square root of 81 all over 2 = -3 +/- 9 all over 2 = 6/2 and -12/2 = 3 , -6 A is the correct answer
\[\LARGE \text{Use:} \;\;\; x_{1/2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\] so we have... \[\LARGE x_{1/2}=\frac{-3\pm \sqrt{3^2-4\cdot 1 \cdot (-18)}}{2\cdot 1}\] \[\LARGE x_{1/2}=\frac{-3\pm \sqrt{81}}{2}\] \[\LARGE x_{1/2}=\frac{-3\pm 9}{2}\] \[\LARGE x_1 =3 , \;\;\;\;\; x_2=-6\]
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