9. x2 - 5x = -6 quadratic formula 10. 2m2 - 7m + 3 = 0 quadratic formulaNeed ko ...

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james8873 @james8873

September 2022 1 0 Report

9. x2 - 5x = -6 quadratic formula
10. 2m2 - 7m + 3 = 0 quadratic formula

Need ko

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✏️QUADRATIC EQUATION

Solve for the roots of the following quadratic equations using the quadratic formula.

- The standard form of a quadratic equation is ax² + bx + c = 0, where a, b are the coefficients, x/y is the variable, and c is the constant term.

9. x² - 5x = - 6

Standard form: $\: \large \tt{ \green { {x}^{2} - 5x + 6 = 0}}$

Values: $\: \tt{ \green{a = 1, \: b = - 5, \: c = 6 }}$

$\large \sf{x = \frac{ - b \: ± \: \sqrt{ {b}^{2} - 4ac } }{2a} }$

$\large \sf{x = \frac{ - ( - 5) \: ± \: \sqrt{( - 5)^{2} - 4(1)(6)} }{2(1)} }$

$\large \sf{x = \frac{ 5 \: ± \: \sqrt{25 - 4(6)} }{2} }$

$\large \sf{x = \frac{ 5\: ± \: \sqrt{25 - 24} }{2} }$

$\large \sf{x = \frac{ 5\: ± \: \sqrt{1} }{2} }$

$\large \sf{x = \frac{ 5\: ± \: 1}{2} }$

$\large \sf{x = \frac{ 5 \: + \: 1}{2} }$ and $\large \sf{x = \frac{ 5\: - \: 1 }{2} }$

$\large \sf{x = \frac{ 6}{2} \: \: and \: x = \frac{4}{2} }$

» $\large \underline { \boxed { \tt \blue{Therefore \: the \: answer \: is \: { \green{x = 3, x = 2}}}}}$

10. 2m² - 7m + 3 = 0

Standard form: $\: \large \tt{ \green { {2m}^{2} - 7m + 3 = 0}}$

Values: $\: \tt{ \green{a = 2, \: b = - 7, \: c = 3 }}$

$\large \sf{x = \frac{ - b \: ± \: \sqrt{ {b}^{2} - 4ac } }{2a} }$

$\large \sf{x = \frac{ - ( - 7) \: ± \: \sqrt{( - 7)^{2} - 4(2)(3)} }{2(2)} }$

$\large \sf{x = \frac{ 7 \: ± \: \sqrt{49 - 4(6)} }{4} }$

$\large \sf{x = \frac{ 7\: ± \: \sqrt{49 - 24} }{4} }$

$\large \sf{x = \frac{ 7\: ± \: \sqrt{25} }{4} }$

$\large \sf{x = \frac{ 7\: ± \: 5}{4} }$

$\large \sf{x = \frac{ 7 \: + \: 5}{2} }$ and $\large \sf{x = \frac{ 7\: - \: 5 }{2} }$

$\large \sf{x = \frac{ 12}{2} \: \: and \: x = \frac{2}{2} }$

» $\large \underline { \boxed { \tt \blue{Therefore \: the \: answer \: is \: { \green{x = 6, x = 1}}}}}$

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