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प्रश्न
`sqrt2x^2+7+5sqrt2=0`
उत्तर
The given equation is `sqrt2x^2+7+5sqrt2=0`
Comparing it with` ax^2+bx+c=0,` we get
`a=sqrt2, b=7 and c=5sqrt2`
∴ Discriminant, `D=b^2-4ac=(7)^2-4xxsqrt2xx5sqrt2=49-40=9>0`
So, the given equation has real roots.
Now, `sqrt(D)=sqrt(9)=3`
∴ `α=(-b+sqrt(D))/(2a)=(-7+3)/(2xxsqrt(2))=-4/(2sqrt2)=-sqrt2`
β=`(-b-sqrt(D))/(2a)=(-7-3)/(2xxsqrt(2))=-4/(2sqrt2)=-sqrt2`
Hence, `-sqrt(2)`and `-(5sqrt2)/2`are the root of the given equation.
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