[數學]f.4數學一問

用根和係數的條件可以比較好地解決

設另一根是α﹐則α+4=3/2=>α=-5/2

然後-(k-6)/2=4α=>k=-8α+6=>k=26

myisland8132已提供最快方法.

In examination, you need to get maximum marks in minimum time.

I suggest you to follow my approach in problem solving:
[ Doing 1) first before attempting 2) ]

1) [ x = 4 is a root ==> x = 4 satisfies the given quadratic equation ]

Put x = 4 into 2x^2 - 3x = k - 6:

2( 4 )^2 - 3( 4 ) = k - 6
2( 16 ) - 12 + 6 = k
k = 32 - 12 + 6
k = 26
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2) [ Method 1 -- Use Sum of roots to find the second root ]

4 + Second root = - ( -3 )/2
4 + Second root = 1.5
Second root = - 2.5
===============

[ Method 2 -- Solve the quadratic equation directly ]

The quad. eq. becomes 2x^2 - 3x - 20 = 0
( 2x + 5 )( x - 4 ) = 0
x = -2.5 or x = 4 ( rejected for the first root is 4 )
Hence, the second root is -2.5
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I am sure solving 'k' is faster, so using my method can make sure you get the basic marks within 30 seconds before looking for the second roots. Can you understand what I mean?

Hope I have helped you.

2x²-3x=k-6x = 42 (4)^2- 3(4) = k-62 (16) - 12 = k - 632 -12 = k - 620 = k - 6k = 26另一個根2x²-3x=k-62x^2 - 3x = 26-62x^2-3x = 202x^2-3x-20=0
(x-4)(x+2.5)
x=4 or x=-2.5