Solve x^2 -6x +5 = 0 and plot this graph between -10<x>10
To solve the equation you need to factorise the quadratic. This means you need to find 2 numbers that when multiplied make 5 and when added together make -6. These would be -1 and -5. You can now separate -6x into -x-5x.
x2-x-5x+5=0. Now you need to factorise (x2-x) and (-5x+5) separately. This gives x(x-1) and -5(x-1)
x(x-1)-5(x-1)=0. you can now factorise the matching brackets (x-1) to give: (x-1)(x-5)=0. to solve for x you need to make each bracket =0 individually and find x.
So, x-1=0 ... x=1
x-5=0 ... x=5
So the answer is x=5 and x=1
To plot the graph, replace 0 with y to get y=x2-6x+5. Choose values for x between -10 and 10 increasing in 2 each time and use the equation to find the value of y for each x. Plot these coordinates on a graph and join up the dots to give you a quadratic.
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