Advertisements
Advertisements
Question
Is there any real value of 'a' for which the equation x2 + 2x + (a2 + 1) = 0 has real roots?
Solution
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
RELATED QUESTIONS
Find the consecutive even integers whose squares have the sum 340.
The difference of squares of two number is 88. If the larger number is 5 less than twice the smaller number, then find the two numbers.
Solve the equation using the factorisation method:
`(3x -2)/(2x -3) = (3x - 8)/(x + 4)`
One fourth of a herd of camels was seen in the forest. Twice the square root of the herd had gone to mountains and the remaining 15 camels were seen on the bank of a river. Find the total number of camels.
Solve the following quadratic equation by factorisation:
9x2 - 3x - 2 = 0
Solve the following by reducing them to quadratic equations:
`sqrt(x/(1 -x)) + sqrt((1 - x)/x) = (13)/(6)`.
In each of the following determine whether the given values are solutions of the equation or not.
x2 + `sqrt(2)` - 4 = 0; x = `sqrt(2)`, x = -2`sqrt(2)`
In each of the following, determine whether the given values are solution of the given equation or not:
x2 - 3x + 2 = 0; x = 2, x = -1
Solve the following equation by factorization
5x2 – 8x – 4 = 0 when x∈Q
(x – 3) (x + 5) = 0 gives x equal to ______.
