All equations of the form ax² + bx + c = 0 can be solved using the quadratic formula:
[tex]\boxed{ \bold{ \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a} } }[/tex]
Determine the values of "a", "b", and "c".
a = 3
b = 5
c = -2
Substituting in the formula:
[tex] \implies \sf x = \frac{ - 5 \pm \sqrt{ {5}^{2} - 4(3)( - 2) } }{2(3)} \\ [/tex]
[tex] \implies \sf x = \frac{ - 5 \pm \sqrt{49} }{6} \\ [/tex]
[tex] \implies \sf x = \frac{ - 5 \pm7}{6} \\ [/tex]
[tex] \implies \sf x = \frac{ - 5 + 7}{6} = \frac{1}{3} \: \: or \: \: x = \frac{ - 5 - 7}{6} = - 2 \\ [/tex]
If [tex] \sf x = \frac{1}{3} : \: \: 3 \bigg( \frac{1}{3} \bigg) {}^{2} + 5 \bigg( \frac{1}{3} \bigg) - 2 = 0 \\ [/tex]
If [tex]\sf x = - 2 : \: \: 3( - 2) {}^{2} + 5( - 2) - 2 = 0[/tex]
Thus, the roots are [tex] \sf {x_1 = \frac{1}{3} } \\ [/tex] and [tex] \sf{x_2 = - 2}[/tex].
Find the roots of 3x² + 5x - 2 = 0.
Thus, the roots are
[tex]\begin{gathered} \sf {x_1 = \frac{1}{3} } \\ \end{gathered} [/tex]
and
[tex]\sf{x_2 = - 2}[/tex].
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SOLUTION:
All equations of the form ax² + bx + c = 0 can be solved using the quadratic formula:
[tex]\boxed{ \bold{ \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a} } }[/tex]
Determine the values of "a", "b", and "c".
a = 3
b = 5
c = -2
Substituting in the formula:
[tex] \implies \sf x = \frac{ - 5 \pm \sqrt{ {5}^{2} - 4(3)( - 2) } }{2(3)} \\ [/tex]
[tex] \implies \sf x = \frac{ - 5 \pm \sqrt{49} }{6} \\ [/tex]
[tex] \implies \sf x = \frac{ - 5 \pm7}{6} \\ [/tex]
[tex] \implies \sf x = \frac{ - 5 + 7}{6} = \frac{1}{3} \: \: or \: \: x = \frac{ - 5 - 7}{6} = - 2 \\ [/tex]
Checking:
If [tex] \sf x = \frac{1}{3} : \: \: 3 \bigg( \frac{1}{3} \bigg) {}^{2} + 5 \bigg( \frac{1}{3} \bigg) - 2 = 0 \\ [/tex]
If [tex]\sf x = - 2 : \: \: 3( - 2) {}^{2} + 5( - 2) - 2 = 0[/tex]
Thus, the roots are [tex] \sf {x_1 = \frac{1}{3} } \\ [/tex] and [tex] \sf{x_2 = - 2}[/tex].
Question:
Find the roots of 3x² + 5x - 2 = 0.
Answer:
Thus, the roots are
Thus, the roots are
[tex]\begin{gathered} \sf {x_1 = \frac{1}{3} } \\ \end{gathered} [/tex]
and
[tex]\sf{x_2 = - 2}[/tex].