Question

If x-3 is a factor of (i) x²+kx+2 (ii) 2x? - kx - 5
Find the value of k in each case.
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Answer 1

$\large { \underline{ \bf \red{Question:- }}}$

If x-3 is a factor of (i) x²+kx+2 (ii) 2x? - kx - 5

Find the value of k in each case.

$\large { \underline{ \bf \purple{Solution:- }}}$

$Let p(x)=x3+kx2−2x+k4</p><p></p><p>$

$As x+k  \: is \: a \: factor</p><p></p><p>$

$Therefore, \: p(−k)=0</p><p></p><p>$

$p(−k) \\ =−k3+k3+2k+k+4 \\ ⇒3k+4</p><p></p><p></p><p>$

$As 3k+4=0</p><p></p><p>$

$\large { \underline{ \bf \pink{Therefore:- }}}$

$∴ \: k = \frac{ - 4}{3}$