Advertisements
Advertisements
प्रश्न
Is there any real value of 'a' for which the equation x2 + 2x + (a2 + 1) = 0 has real roots?
Advertisements
उत्तर
Let quadratic equation x2 + 2x + (a2 + 1) = 0has real roots.
Here, a = 1, b = 2 and ,c = (a2 + 1)
As we know that `D = b^2 - 4ac`
Putting the value of a = 1, b = 2 and ,c = (a2 + 1), we get
\[D = \left( 2 \right)^2 - 4 \times 1 \times \left( a^2 + 1 \right)\]
\[ = 4 - 4\left( a^2 + 1 \right)\]
\[ = - 4 a^2\]
The given equation will have equal roots, if D > 0
i.e.
\[- 4 a^2 > 0\]
\[ \Rightarrow a^2 < 0\]
which is not possible, as the square of any number is always positive.
Thus, No, there is no any real value of a for which the given equation has real roots.
APPEARS IN
संबंधित प्रश्न
Solve the equation `4/x-3=5/(2x+3); xne0,-3/2` for x .
A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was Rs 750. We would like to find out the number of toys produced on that day.
If an integer is added to its square, the sum is 90. Find the integer with the help of quadratic equation.
An aeroplane left 50 minutes later than its scheduled time, and in order to reach the destination, 1250 km away, in time, it had to increase its speed by 250 km/hr from its usual speed. Find its usual speed.
The area of a right angled triangle is 165 m2. Determine its base and altitude if the latter exceeds the former by 7 m.
Sum of the areas of two squares is 640 m2. If the difference of their perimeters is 64 m. Find the sides of the two squares.
For the equation given below, find the value of ‘m’ so that the equation has equal roots. Also, find the solution of the equation:
(m – 3)x2 – 4x + 1 = 0
The sum of natural number and its reciprocal is `65/8` Find the number
One of the roots of equation 5m2 + 2m + k = 0 is `(-7)/5` Complete the following activity to find the value of 'k'.
If \[x = - \frac{1}{2}\],is a solution of the quadratic equation \[3 x^2 + 2kx - 3 = 0\] ,find the value of k.
If the sum of the roots of the equation x2 − x = λ(2x − 1) is zero, then λ =
A two digit number is such that the product of the digits is 14. When 45 is added to the number, then the digit are reversed. Find the number.
The sum of the square of two numbers is 233. If one of the numbers is 3 less than twice the other number. Find the numbers.
Five years ago, a woman’s age was the square of her son’s age. Ten years hence, her age will be twice that of her son’s age. Find:
- the age of the son five years ago.
- the present age of the woman.
Solve the following equation by factorization
2x2 – 9x + 10 = 0,when x∈N
Solve the following equation by factorization
`4sqrt(3)x^2 + 5x - 2sqrt(3)` = 0
Solve the following equation by factorization
`x^2 - (1 + sqrt(2))x + sqrt(2)` = 0
Find the values of x if p + 7 = 0, q – 12 = 0 and x2 + px + q = 0,
If the sum of the roots of the quadratic equation ky2 – 11y + (k – 23) = 0 is `13/21` more than the product of the roots, then find the value of k.
For equation `1/x + 1/(x - 5) = 3/10`; one value of x is ______.
