Advertisements
Advertisements
प्रश्न
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
उत्तर
Word problem:
The product of two consecutive natural numbers is 30. Find the numbers.
Answer:
Let the first natural number be x.
∴ The second consecutive natural number = x + 1
According to the given condition,
x(x + 1) = 30
∴ x2 + x = 30
∴ x2 + x – 30 = 0, which is the required quadratic equation.
संबंधित प्रश्न
The divisor and quotient of the number 6123 are same and the remainder is half the divisor. Find the divisor.
If one root of the equation` 3x^2-10x+3=0 is 1/3` then the other root is
(a) `-1/3` (b) `1/3` (c)`-3` (d)`3`
If one root of `5x^2+13x+k=0` be the reciprocal of the other root then the value of k is
`(a)0 (b)1 (c)2 (d)5`
The roots of the equation `ax^2+bx+c=0` will be reciprocal each other if
(a)a=b (b)b=c (c)=a (d)= none of these
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`
If the roots of the quadratic equation `2x^2+8x+k=0` are equal then find the value of k.
Decide whether the following equation is quadratic equation or not.
`"y"^2 + 1/"y" = 2`
Write the following equation in the form ax2 + bx + c = 0, then write the values of a, b, c for the equation.
(x – 1)2 = 2x + 3
Mr. Kasam runs a small business of making earthen pots. He makes certain number of pots on daily basis. Production cost of each pot is Rs 40 more than 10 times total number of pots, he makes in one day. If production cost of all pots per day is Rs 600, find production cost of one pot and number of pots he makes per day.
Choose the correct answer for the following question.
\[\sqrt{5} m^2 - \sqrt{5}m + \sqrt{5} = 0\] which of the following statement is true for this given equation?
Find the value of m so that the quadratic equation mx (x − 7) + 49 = 0 has two equal roots.
Which of the following is a quadratic equation ?
If 3x + 5y = 9 and 5x + 3y = 7 find the value of x + y.
Write the following equation in the form ax2 + bx + c= 0, then write the values of a, b, c for equation.
P(3+6p) = –5
A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km downstream. Determine the speed of the stream and that of the boat in still water.
Find the value of k for which the quadratic equation kx (x − 2) + 6 = 0 has two equal roots.
In a right-angled triangle, altitude is 2 cm longer than its base. Find the dimensions of the right-angled triangle given that the length of its hypotenuse is 10 cm.
If both the roots of the quadratic equation x2 – 2kx + k2 + k – 5 = 0 are less than 5, then k lies in the interval is ______.
