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## Question

secondary 4 | E Maths

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Sum of roots

= -(-6)/2

= 3

Since roots differ by 5,

First root = second root + 5

Sum = first root + second root

= Second root + 5 + second root

= 2 x second root + 5

2 x second root + 5 = 3

So 2 x second root = 3 - 5 = -2

Second root = -2 ÷ 2 = -1

First root = -1 + 5 = 4

(You can also use first root = second root - 5. The roots will just swap places.

i.e first root will then be -1 and second root will be 4 )

Product of roots

= -k/2= 4 x (-1) = -4

k/2 = 4

k = 2 x 4 =

To check (if you wanna be sure. Or you can also use this as the alternate working for finding k)

x = 4 or x = -1

x - 4 = 0 or x + 1 = 0

So since they are the two roots,

(x - 4)(x + 1) = 0

x² - 3x - 4 = 0

2x² - 6x - 8 = 0

k = 8

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