Advertisements
Advertisements
प्रश्न
Solve `3x^2+5sqrt5x-10=0`
उत्तर
`3x^2+5sqrt5x-10=0`
⇒ `3x^2+6sqrt5x-sqrt5x-10=0`
⇒`3x(x+2sqrt5)-sqrt5(x+2sqrt5)=0`
⇒`(x+2sqrt5) (3x-sqrt5)=0`
⇒`x+2sqrt5=0 or 3x-sqrt5=0`
⇒`x=-2sqrt5 or x=sqrt5/3`
Hence, `-2sqrt5 and sqrt5/3` are the roots of the given equation.
APPEARS IN
संबंधित प्रश्न
If the equation `4x^2-3kx+1=0` has equal roots then value of k=?
(a)`+-2/3` (b)`+-1/3`
(c)` +-3/4` (d) `+-4/3`
The roots of the equation `2x^2-6x+3=0` are
(a) real, unequal and rational (b) real, unequal and irrational (c) real and equal (d) imaginary
Find the value of k so that the quadratic equation` x^2-4kx+k=0`
has equal roots.
If 1 is a root of the equations ay2 + ay + 3 = 0 and y2 + y + b = 0 then ab equals: ?
Product of Pragati’s age 2 years ago and 3 years hence is 84. Find her present age.
The Sum of squares of 2 consecutive natural even numbers is 244; find the numbers.
Solve the following quadratic equation.
x2 - 4x - 3 = 0
Find c if the system of equations cx + 3y + (3 – c) = 0; 12x + cy – c = 0 has infinitely many solutions?
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
A tank can be filled up by two taps in 6 hours. The smaller tap alone takes 5 hours more than the bigger tap alone. Find the time required by each tap to fill the tank separately.
