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प्रश्न
Write any two quadratic equations.
उत्तर
Two quadratic equations are \[x^2 + 10x - 200 = 0\] and \[x^2 + 5x - 6 = 0\].
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संबंधित प्रश्न
The roots of a quadratic equation are 5 and -2. Then, the equation is
(a)`x^2-3x+10=0` (b)`x^2-3x-10=0` (c)x^2+3x-10=0 (d)`x^2+3x+10=0`
Find the roots of the quadratic equation `2x^2-x-6=0`
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\[x + \frac{1}{x} = - 2\]
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Solve for x : `1/(2a + b + 2x) =1/(2a) + 1/b + 1/(2x); x ≠ 0, x ≠ (−2a −b)/2`, a, b ≠ 0
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
If 460 is divided by a natural number, then quotient is 2 more than nine times the divisor and remainder is 5. Find the quotient and divisor.
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.
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.
