Question
If x1 and x2 are the roots of the equation 2x2
+ 3x – 9 = 0, then the equation which has the roots 1/x1 and1/x2 is:Solution
We know that, for a quadratic equation ax2 + bx + c, Sum of its roots = -b/a and product of roots = c/a For 2x2 + 3x – 9 = 0, => x1 + x2 = -3/2 and x1x2 = -9/2 For the equation whose roots are 1/x1 and 1/x2, Sum of roots = (1/x1) + (1/x2) = (x1 + x2)/x1x2 = -3/-9 = 1/3 Product of roots = 1/(x1x2) = -2/9 ∴ the quadratic equation = x2 - 1/3x - 2/9 = 9x2 - 3x - 2 = 0
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