Q In the equation x2+ax-a2-1 = 0 has roots of opposite signs, then determine the interval in which 'a' - Maths - Complex Numbers and Quadratic Equations

Question

Q In the equation x 2 + a x - a 2 - 1   =   0 has roots
of opposite signs, then determine the interval in which 'a' lies

Neha Sethi · Accepted Answer

Dear student
We havex2+ax-a2-1=0Given: Roots of the equation are of opposite signs
⇒The product of roots will be negative
Also, product of roots=constant termcoeff
 of x2=-1+a21 =-1+a2So, Product will be less than 0⇒-1+a2<0⇒1+a2>0⇒a2>-1 for real a, a2is always positive  which is satisfied by above
So a can be any real number ranging from -∞ to +∞So, a lies in -∞,∞
Regards

Q. In the equation x 2 + a x - a 2 - 1 = 0 has roots of opposite signs, then determine the interval in which 'a' lies.

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