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प्रश्न
`25x^2+30x+7=0`
उत्तर
Given:
`25x^2+30x+7=0`
On comparing it with `ax^2+bx+x=0`
a = 25,b = 30 and c = 7
Discriminant D is given by:
`D=(b^2-4ac)`
=`30^2-4xx25xx7`
=`900-700`
=`200`
=`200`
=`200>0`
Hence, the roots of the equation are real.
Roots α and β are given by:
`α=(-b+sqrt(D))/(2a)=(-30+sqrt(200))/(2xx25)=(-30+10sqrt(20))/50=(10(-3+sqrt(2)))/50=((-3+sqrt(2)))/5`
`β=(-b-sqrt(D))/(2a)=(-30-sqrt(200))/(2xx25)=(-30-10sqrt(20))/50=(10(-3-sqrt(2)))/50=((-3-sqrt(2)))/5`
Thus, the roots of the equation are `((-3+sqrt(2)))/5` and `((-3-sqrt(2)))/5`
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