Question

if one root of the quadraticequation 2x+kx+4=0 is 2 then the other root is​

Answer 1

${\huge{\underline{\underline{\sf{\blue{Solution :-}}}}}}$

${\huge{\underline{\underline{\sf{\blue{Given :-}}}}}}$

⠀⠀⠀⠀⠀ • Quadratic equation 2x²+kx+4=0

${\huge{\underline{\underline{\sf{\blue{Answer :-}}}}}}$

⠀⠀⠀⠀⠀ • Other root be 1

${\huge{\underline{\underline{\sf{\blue{To\: Calculate :-}}}}}}$

⠀⠀⠀⠀⠀ • Other root

${\huge{\underline{\underline{\sf{\blue{Explanation :-}}}}}}$

Let α and β be the roots of Quadratic equation

Quadratic equation = 2x²+kx+4=0

${\huge{\underline{\underline{\sf{\blue{Where :-}}}}}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ α= 2

a= 2

b= k

c= 4

⠀⠀⠀⠀⠀ Sum of roots = -b/a

α+β = -b/a

➡️ 2+ β = -k/2

➡️ β = -k/2 -2

➡️ β = -k-4/2

⠀⠀⠀⠀⠀ Product of roots = c/a

α.β = c/a

➡️ 4/2

➡️ 2

Putting values of β = -k-4/2 in above

2×-k-4/2=2

➡️ (-k-4)=2

➡️ k= -4-2

➡️ k= -6

Putting the value of k in β = -k-4/2

β = -k-4/2

➡️ β = -(-6) -4 /2

➡️ β = 6-4/2

➡️ β = 2/2

➡️ β= 1

${\huge{\underline{\underline{\sf{\blue{Hence :-}}}}}}$

⠀⠀⠀⠀ • Other root be 1

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