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
A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.
Solve the following quadratic equations by factorization:
9x2 − 3x − 2 = 0
A two-digit number is such that the products of its digits is 8. When 18 is subtracted from the number, the digits interchange their places. Find the number?
The sum of two numbers is 18. The sum of their reciprocals is 1/4. Find the numbers.
Three consecutive positive integers are such that the sum of the square of the first and the product of other two is 46, find the integers.
The time taken by a person to cover 150 km was 2.5 hrs more than the time taken in the return journey. If he returned at a speed of 10 km/hr more than the speed of going, what was the speed per hour in each direction?
`x^2+8x-2=0`
If the equation x2 − bx + 1 = 0 does not possess real roots, then
If the sum of the roots of the equation x2 − x = λ(2x − 1) is zero, then λ =
Solve the following equation : `"x"^2 - 4 sqrt 2 "x" + 6 = 0 `
A two digit number is such that the product of its digit is 8. When 18 is subtracted from the number, the digits interchange its place. Find the numbers.
A farmer wishes to grow a 100m2 rectangular vegetable garden. Since he was with him only 30m barbed wire, he fences 3 sides of the rectangular garden letting the compound of his house to act as the 4th side. Find the dimensions of his garden .
The length of verandah is 3m more than its breadth. The numerical value of its area is equal to the numerical value of its perimeter.
(i) Taking x, breadth of the verandah write an equation in ‘x’ that represents the above statement.
(ii) Solve the equation obtained in above and hence find the dimension of verandah.
Solve the following equation and give your answer up to two decimal places:
x2 − 5x − 10 = 0
The speed of an express train is x km/hr arid the speed of an ordinary train is 12 km/hr less than that of the express train. If the ordinary train takes one hour longer than the express train to cover a distance of 240 km, find the speed of the express train.
Solve the following equation by factorization
2x2 – 9x + 10 = 0,when x∈N
Find the values of x if p + 7 = 0, q – 12 = 0 and x2 + px + q = 0,
A rectangular garden 10 m by 16 m is to be surrounded by a concrete walk of uniform width. Given that the area of the walk is 120 square metres, assuming the width of the walk to be x, form an equation in x and solve it to find the value of x.
A piece of cloth costs Rs. 300. If the piece was 5 metres longer and each metre of cloth costs Rs. 2 less, the cost of the piece would have remained unchanged. How long is the original piece of cloth and what is the rate per metre?
The speed of a boat in still water is 11 km/ hr. It can go 12 km up-stream and return downstream to the original point in 2 hours 45 minutes. Find the speed of the stream
