Question 119

If (x-1) and (x+3) are the factors of $$x^{2}+k_{1}x + k_{2}$$ then

Solution

METHOD1:

If (x-1) and (x+3) are the factors of $$x^{2}+k_{1}x + k_{2}$$

then its zeros are 1, -3

sum of zeros = $$-k_{1}=-2\rightarrow k_{1}=2$$

product of zeros = $$k_{2}=-3\rightarrow k_{2}=-3$$

so the answer is option B.

METHOD2:

Multiply (x-1) and (x+3)

= $$x^{2}-x+3x-3$$

= $$x^{2}+2x-3$$

now, compare $$x^{2}+2x-3$$ with $$x^{2}+k_{1}x + k_{2}$$

$$k_{1}=2$$ and $$k_{2}=-3$$

so the answer is option B.

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