Topic 1 - Simultaneous Equations
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Transcript of Topic 1 - Simultaneous Equations
1) Solving a pair of simultaneous linear equationsExample 1
Method 1 : By Elimination Method 2 : By Substitution
2) Solving a pair of simultaneous linear and non-linear equations
Example 2Solve the simultaneous equations
Solution
3) Find the point(s) of intersection of two graphs algebraically
Example 3Find the coordinates of the points of intersection of the line and the curve
Solution
4) Formulate and solve simultaneous equations to model real-world problems
Example 4A rectangular car license plate has an area of 600 cm2. Its perimeter is 4 cm more than 10 times its height. Find the dimensions of this license plate.
Solution
Class Exercise 11) Solve the simultaneous equations
2) Find the coordinates of the points of intersection of the line and the curve
3) A rectangular picture frame has an area of 154 cm2 and a perimeter of 50 cm. Find the dimensions of this picture frame.
Consider the equation ax2 + bx + c = 0, where a(1)If its roots α and β , (x – α)(x – β) = 0 Expanding, we have: x2 – αx – βx + αβ = 0 x2 – (α + β)x + αβ = 0 So, if we compare the above with (1):
Result: and
Recall that a quadratic equation with roots α and β can be written as
(x – α)(x – β) = 0 or x2 – (α + β)x + αβ = 0.
Thus if you know the sum and product of its roots, you can write the equation as follows :-
x2 – (sum of roots)x + (product of roots) = 0
1) Use the formulae for the sum and product of roots of a quadratic equation
Example 1The roots of the quadratic equation are α and β. Findi) the sum and product of its rootsii) the value of iii) the value of (2α +1)(2β+1) Solution
Example 3The quadratic equation has non-zero roots which differ by 2. Find the value ofi) each rootii) the constant k Solution
2) Form a quadratic equation from its roots Example 4The roots of the quadratic equation are α and β. Find the quadratic equation whose roots are α2
and β2. Solution
Class Exercise 11) The roots of the quadratic equation are α and β. Findi) the sum and product of its rootsii) the value of iii) the value of (α - 2)(β - 2)
2) The roots of the quadratic equation are α and β. Find the value ofi) ii)iii) 3) The quadratic equation has non-zero roots which differ by 1. Find the value ofi) each rootii) the constant k4) The roots of the quadratic equation are α and β. Find the quadratic equation whose roots are (3α +1) and (3β+1).