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"Grade 12 Equation Solving: Comprehensive Summary and Techniques"
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Title: Grade 12 Equation Solving: Comprehensive Summary and Techniques Description: The document "Grade 12 Equation Solving: Comprehensive Summary and Techniques" provides a detailed and comprehensive overview of various equation-solving methods specifically tailored for the Grade 12 level. Thi...

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  • June 8, 2023
  • 4
  • 2022/2023
  • Summary

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A quadratic equation is an algebraic equation of the second degree in x. The
2
quadratic equation in its standard form is 𝑎𝑥 + 𝑏𝑥 + 𝑐 = 0, where a and b are
the coefficients, x is the variable, and c is the constant term.

Solving Quadratic Equations:

-Quadratic equations can be factored

-Completing the square

2
−𝑏± 𝑏 −4𝑎𝑐
-You can use the quadratic formula: 2𝑎



When the Discriminant (△ = 𝑏 − 4𝑎𝑐) is(Nature Of Roots):
2



*positive(∆ > 0), there are 2 real solutions,rational(∆ = 𝑝𝑒𝑟𝑓𝑒𝑐𝑡 square), Unequal(∆ ≠ 0)

Irrational(∆ ≠ 𝑝𝑒𝑟𝑓𝑒𝑐𝑡 𝑠𝑞𝑢𝑎𝑟𝑒), Unequal(∆ ≠ 0)

*zero(∆ = 0), there is one real solution,rational(∆ = 𝑝𝑒𝑟𝑓𝑒𝑐𝑡 𝑠𝑞𝑢𝑎𝑟𝑒),Equal

*negative(∆ < 0),non-real, there are 2 complex solutions

I will now show you how to solve quadratic equations.

(𝑖)2𝑥(4𝑥 − 1) = 15
Multiply out/ Use the distributive law
2
8𝑥 − 2𝑥 − 15 = 0
Factorise
(2𝑥 − 3)(4𝑥 + 5) = 0
Apply the zero factor law
2𝑥 − 3 = 0 𝑜𝑟 4𝑥 + 5 = 0
Solve for 𝑥
2𝑥 3 4𝑥 −5
2
= 2
𝑜𝑟 4
= 4
3 5
𝑥= 2
𝑜𝑟 𝑥 =− 4
2
(𝑖𝑖)𝑥 + 21𝑥 + 10 = 0
Subtract 10 on both sides of the equation
2
𝑥 + 21𝑥 =− 10
𝑏 2
Add ( 2 ) to both sides of the equation

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