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प्रश्न
Solve for x: `3x^2-2sqrt6x+2=0`
उत्तर
The given quadratic equation is `3x^2-2sqrt6x+2=0`
Comparing with the quadratic equation ax2 + bx + c = 0, we have
`a=3,b=-2sqrt6` and `c=2`
Discriminant of the given quadratic equation,
`D=b^2-4ac=(2sqrt6)^2-4xx3xx2=24-24=0`
`therefore x=((-2sqrt6)^2+-sqrt0)/(2xx3)` `therefore x=(-b+-sqrtD)/(2a)`
`rArr x=2sqrt6/6`
`rArrx=sqrt6/3`
Thus, the solution of the given quadratic equation is `x=sqrt6/3`.
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संबंधित प्रश्न
Which of the following is a quadratic equation?
(a) `x^3-3sqrtx+2=0` (b) `x+1/x=x^2`
(c)` x^2+1/x^2=5` (d) `2x^2-5x=(x-1)^2`
The roots of `ax^2+bx+c=0`,a≠0 are real and unequal, if `(b^2-4ac)` is
(a)>0 (b)=0 (c)<0 (d)none of these
If the equation `x^2-5x+1=0` has no real roots then
(a)`k<-2`
(b)`k>2`
(c) `-2<k<2`
(d) None of these
The roots of the quadratic equation `2x^2-x-6=0`
(a)`-2, 3/2` (b) `2, -3/2`
(c)` -2, 3/2` (d) `2, 3/2`
Write any two quadratic equations.
Choose the correct answer for the following question.
One of the roots of equation x2 + mx – 5 = 0 is 2; find m.
Mr. Dinesh owns an agricultural farm at village Talvel. The length of the farm is 10 meter more than twice the breadth. In order to harvest rain water, he dug a square shaped pond inside the farm. The side of pond is `1/3` of the breadth of the farm. The area of the farm is 20 times the area of the pond. Find the length and breadth of the farm and of the pond.
If in an A. P., d = 10, find t6 - t2.
Find k, one of the roots of the quadratic equation kx2 - 7x + 12 = 0 is 3.
Form a quadratic equation such that one of its roots is 5. Form a quadratic equation for it and write. (For the formation of word problems you can use quantities like age, rupees, or natural numbers.) (Sample solution for the above example is given below students can take another number to form another example)
Solution:
We need one of the solutions of the quadratic equation as 5.
Then we can take another root as any number like a positive or negative number or zero. Here I am taking another root of the quadratic equation as 2.
Then we can form a word problem as below,
Smita is younger than her sister Mita by 3 years (5 – 2 = 3). If the product of their ages is (5 × 2 = 10). Then find their present ages.
Let the age of Mita be x.
Therefore age of Smita = x – 3
By the given condition,
x(x – 3) = 10
x2 – 3x – 10 = 0
