Question

if one zero of the polynomial 2x²-5x-(2k+1) is twice the other , find both the zeroes of the polynomial and the value of k

Answer 1

Hii User!!

Let, p(x)=2x²-5x-(2k+1). =) eq (i)

Also let, α be one root of equation (i)
=)Then the other root will be 2α.

=)α+2α=-(-5)/2
=) 3α=5/2
=) α=5/6

Here ,α×2α=-(2k+1)/2

=) 2α²=-(2k+1)/2

=) -(2k+1)/2=2×(5/6)²

=) -(2k+1)=4×25/36
=)-2k-1=25/9

= -2k=25/9+1
=) -2k=34/9
=)  k=-34/9×1/2

=) k=-17/9


Hence, the value of k is -17/9


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