If the equation x^3 - ax^2+bx - a=0 has 3 real roots then which of the following is true a) a=1. d) a ( not equal) 1 c) b=1. d) b( not equal) 1
Answers
it is given that equation x³ - ax² + bx - a = 0 has three real roots.
we have to find the condition in which equation has real roots.
x³ - ax² + bx - a = 0
⇒x²(x - a) + (bx - a) = 0
when we take b = 1,
x²(x - a) + (x - a) = 0
⇒(x² + 1)(x - a) = 0
here x² + 1 ≠ 0 so x has two imaginary roots if b = 1. but a/c to question, all roots are real.
therefore, b must not equal to 1. i.e., b ≠ 1 for real value of x.
hence option (d) is correct choice.
also read similar questions : If the equation x² − bx + 1 = 0 does not possess real roots, then
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