Find the equation whose roots are \(\frac{2}{3}and \frac{-1}{4}\)
a
\(12x^2-5x+2=0\)
b
\(12x^2-11x+2=0\)
c
\(x^2-\frac{11}{12}x+2=0\)
d
\(x^2+\frac{11}{12}x-2=0\)
e
\(12x^2+11x+2=0\)
Explanation
Correct Option
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Discussions (4)
Igber
6 years ago
x^2 - (sum of given roots )x + (product of given roots ) = 0
=> x^2 - (2/3 -1/4)x + (2/3 * -1/4) = 0
=> x^2 -2/3x +1/4x - 2/12 = 0
=> x^2 - 11/12x- 2/12 = 0
=> 12x^2 -11x - 2 = 0
Jeffersonv
11 years ago
option A and E can only be correct if and only if 2/3 is negative. that is if the two roots are -2/3 and -1/4 hence, there is no option.
crypticblake
3 years ago
Option A should be 12x^2 − 5x − 2 = 0 instead of 12x^2 − 5x + 2 = 0, as my workings and the explanation here shows.
