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. Find the roots of the following quadra...

. Find the roots of the following quadratic equation : `x^2 - 3 sqrt5 x + 10 = 0`

Text Solution

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Given equation is `x^(2)-3sqrt(5)x+10=0`
On comparing with `ax^(2)+bx+c=0` we have
`a=1, b=-3sqrt(5)` and `c=10`
By quadratic formula `x=(-b+-sqrt(b^(2)-4ac))/(2a)`
`=(-(-3sqrt(5))+-sqrt((-3sqrt(5))^(2)-4(1)(10)))/(2(1))`
`=(3sqrt(5)+-sqrt(45-10))/2=(3sqrt(5)+-sqrt(5))/2`
`=(3sqrt(5)+sqrt(5))/2,(3sqrt(5)-sqrt(5))/2=2sqrt(5),sqrt(5)`
So `2sqrt(5)` and `sqrt(5)` are the roots of the given equation.
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