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Question

If the equation 2x2+kr5=0 and x23x4=0 have a common root, then the value of k is

A
2
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B
3
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C
274
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D
14
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Solution

The correct options are
B 3
C 274
2x2+kx5=0
letα,βbetherootsthenc
α+β=k2
αβ=52
x23x4=0
(x4)(x+1)=0
x=4,1
α=1,β=4
ifcommonrootis1
(1)β=52
β=52
1+52=k2
2+52=k2
k=3
ifcommonrootis4
(4)β=52
β=58
458=k2
3258=k2
k=274

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