Question
If α and β are the roots of the equation x2 + px + q = 0 and α4 and β4 are the roots of the equation x2– rx + s = 0, then the equation x2 – 4qx + 2q2 – r = 0 has always:
Answer: Option D
:
D
Given question isflexible. So, we can assume the roots and can make an other quardatic equation.
Let α = 1 and β = 2, then the expression becomes x2 – 3x + 2 = 0. So p = -3, q = 2, r = 17, s = 16. The new expression is x2 – 8x – 9 = 0. 1 root is positive and other is negative.
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:
D
Given question isflexible. So, we can assume the roots and can make an other quardatic equation.
Let α = 1 and β = 2, then the expression becomes x2 – 3x + 2 = 0. So p = -3, q = 2, r = 17, s = 16. The new expression is x2 – 8x – 9 = 0. 1 root is positive and other is negative.
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