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5x^2+px+q=0
Or, 5*-2^2+p*-2+q=0....... 5*-1/5^2+-p/5+q=0
Or, 20+-2p+q=0............... 1/5+-p/5+q=0
Or, -2p+q= -20.................... -p/5+q=-1/5
Or,p+q=20/-2= 10...............Or, p+q=1
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Answer:
p = 11 and q = 2
Step-by-step explanation:
We have,
5x² + px + q = 0
also,
x = (-2) and x = (-1/5)
Let p(x) = 5x² + px + q
Now, when x = (-2)
p(-2) = 5(-2)² + p(-2) + q
As x = (-2) is a solution, p(-2) = 0
0 = 5(4) - 2p + q
0 = 20 - 2p + q
2p - 20 = q
q = 2p - 20 ----- 1
Also,
p(-1/5) = 5(-1/5)² + p(-1/5) + q
0 = 5(1/25) - (p/5) + q
0 = (1/5) - (p/5) + q
0 = (1/5) - (p/5) + (5q/5)
Now multiplying the whole equation by 5,
1 - p + 5q = 0
p - 5q = 1 ------ 2
Substituting eq.1 in eq.2,
p - 5(2p - 20) = 1
p - 10p + 100 = 1
-9p = 1 - 100
-9p = -99
p = (-99/-9)
p = 11
Putting p = 11, in eq.1,
q = 2(11) - 20
q = 22 - 20
q = 2
Hence,
p = 11 and q = 2
Hope it helped and believing you understood it........All the best