Q.If the roots of the equation ( ???? + 2 ) ???? 2 − ( ???? − 3 ) ???? + 3 ???? − 1 = 0 are equal in magnitude but opposite in sign, what is the value of ???? ? (a) -3 (b) 1 (c) 3 (d) None of the above
Answer: C
Given the equation: \((p+2)x^2 - (p-3)x + 3p - 1 = 0\) Let the roots be \(\alpha\) and \(\beta\), which are equal in magnitude but opposite in sign. So, \(\alpha + \beta = 0\) ⇒ \(-\frac{-(p-3)}{p+2} = 0\) ⇒ \(p - 3 = 0\) ⇒ \(p = 3\)
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