Share
Notifications

View all notifications
Advertisement

Is There Any Real Value of 'A' for Which the Equation X2 + 2x + (A2 + 1) = 0 Has Real Roots? - Mathematics

Login
Create free account


      Forgot password?

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.

  Is there an error in this question or solution?
Advertisement

APPEARS IN

 RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 4: Quadratic Equations
Q: 7 | Page no. 82
 RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 4: Quadratic Equations
Q: 7 | Page no. 82
Advertisement
Is There Any Real Value of 'A' for Which the Equation X2 + 2x + (A2 + 1) = 0 Has Real Roots? Concept: Solutions of Quadratic Equations by Factorization.
Advertisement
View in app×