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If the equation X^2 +aX - a^2-1 =0 will have roots of opposite sign if (1) a belongs to (-∞, ∞) (2) a belongs to [-1,1]

If the equation X^2 +aX - a^2-1 =0 will have roots of opposite sign if (1) a belongs to (-∞, ∞) (2) a belongs to [-1,1]

Grade:12th pass

1 Answers

Subhash Kumar
11 Points
6 years ago
If the roots are of opposite sign then their product will be negative.And product= constant/coefficient of x^2So,Product is less than 0→-(a^2+1) is less than 0→a^2+1 is greater than 0→a^2 is greater than -1For real a,a^2 is always nonnegative.Which is satisfied by the above. So a can be any real number ranging from - infinity to + infinity.Hence option (a) is correct.

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