If the equation x2 5x 6 and x2 kx 1 0 have a common root then what is the value of k ........

Quantitative Aptitude (CDS) Quadratic Equations

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If the equation x²+5x+6 and x²+kx+1=0 have a common root , then what is the value of k?

$-\frac{5}{2}\: or-\frac{10}{3}$

$\frac{5}{2}\: or\: \frac{10}{3}$

$\frac{5}{2}\: or-\frac{10}{3}$

$-\frac{5}{2}\: or\: \frac{10}{3}$

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Explanation:

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a₁x²+b₁x+c1=0
a₂x²+b₂x+c2=0
for common roots
(c₁a₂ -a₁c₂)² = (b₁c₂ - c₁b₂)(a₁b₂-b₁a₂)
So for x²+5x+6 and x²+kx+1=0
(6.1-1.1)²= (5.1-6.k)(1.k-5.1)=(5)² = (5-6k)(k-5)
=> 25= -6x²+35k - 25
=> 6k² -35k+50=0
k = 5/2 , k=10/3