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A line through the origin intersects the...

A line through the origin intersects the parabola `5y=2x^(2)-9x+10` at two points whose x-coordinates add up to 17.
Then the slope of the line is __________ .

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Verified by Experts

The correct Answer is:
5
(5) Let the line be
y=mx (1)
solving it with `5y=2x^(2)-9x+10`, we get
`or2x^(2)-(9+5m)x+10=0`
Sum of roots `=(9+5m)/(2)=17`
`or9+5m=34`
`or5m=25`
`orm=5`
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