Question

For what value of k, equation: 2x^2+kx-5 = 0 & x^2 - 3x - 4 = 0 may have one root common.

Answer 1

X^2--3x--4=0

x^2--4x+x-4=0

x (x--4)+1(x--4)=0

(x+1)(x--4)=0

x+1=0 |x--4=0

x=-1 , | x=4

when x=--1

then,

2x^2+kx--5=0

(2×--1×--1)+k×--1=5

2--k=5

k=2--5

=--3

when x=4

.

. . 2x^2+kx--5=0

(2×4×4)+4k=5

4k+32=5

4k =5--32

4k=--27

k=--27/4

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