Question

3. Find the value of k for which x=1 is a root of the equation x2 +kx+3 = 0.
Also, find the other root.
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Answer 1

⠀⠀⠀⠀⠀⠀${\huge{\underbrace{\rm{Question}}}}$

Find the value of k for which x=1 is a root of the equation x2 +kx+3 = 0 Also find the other root.

⠀⠀⠀⠀⠀⠀⠀${\huge{\underbrace{\rm{Answer}}}}$

Given:

⠀⠀

• Given equation is x² + Kx + 3 = 0

• value of x is 1

⠀⠀

To find:

⠀⠀

• Find the value of k

• find the other root

⠀⠀

Solution:

⠀⠀

Given equation is x² + Kx + 3 = 0

now putting the value of x

⠀⠀

⠀⠀⠀⠀⠀$\sf{:\implies x^{2}+Kx+3=0}$

⠀⠀

⠀⠀⠀⠀⠀$\sf{:\implies (1)^{2}+k×1+3=0}$

⠀⠀

⠀⠀⠀⠀⠀$\sf{:\implies 1+k+3=0}$

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⠀⠀⠀⠀⠀$\sf{:\implies k+4=0}$

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⠀⠀⠀⠀⠀⠀$\boxed{\bf{\pink{:⟹k=\:-4}}}$

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Now,

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⠀⠀⠀⠀⠀⠀$\sf{Putting\:the\:value\:of\:k}$

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⠀⠀⠀⠀⠀$\sf{:\implies x^{2}+(-4)x+3=0}$

⠀

⠀⠀⠀⠀⠀$\sf{:\implies x^{2}-4x+3=0}$

⠀

⠀⠀⠀⠀⠀$\sf{:\implies x^{2}-(3+1)x+3=0}$

⠀⠀

⠀⠀⠀⠀⠀$\sf{:\implies x^{2}-3x-x+3=0}$

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⠀⠀⠀⠀⠀$\sf{:\implies x(x-3)-1(x-3)=0}$

⠀⠀

⠀⠀⠀⠀⠀$\sf{:\implies (x-3)(x-1)=0}$

⠀⠀

⠀⠀⠀⠀⠀$\sf{:\implies x = 3\:,\:\:1}$

⠀⠀

Therefore,

⠀⠀⠀⠀⠀⠀•⠀The value of k is - 4

⠀⠀⠀⠀⠀⠀•⠀the other root is 3

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