Advertisements
Advertisements
Question
`sqrt2x^2+7+5sqrt2=0`
Solution
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.
APPEARS IN
RELATED QUESTIONS
In the following, determine whether the given quadratic equation have real roots and if so, find the roots:
3x2 - 2x + 2 = 0
In the following, determine whether the given quadratic equation have real roots and if so, find the roots:
`2x^2-2sqrt6x+3=0`
In the following, determine whether the given quadratic equation have real roots and if so, find the roots:
3x2 - 5x + 2 = 0
Find the value of a and b for which `x=3/4`and `x =-2` are the roots of the equation `ax^2+bx-6=0`
`2x^2+x-6=0`
`11-x=2x^2`
`x^2-2ax-(4b^2-a^2)=0`
`a^2b^2x^2-(4b^4-3a^4)x-12a^2b^2=0,a≠0 and b≠ 0`
Find the value of k for which the roots of `9x^2+8kx+16=0` are real and equal
Find the discriminant of the quadratic equation 4x2 – 5 = 0 and hence comment on the nature of roots of the equation.
