Question

3x²-kx + 6 = 3
find the value of k​

Answer 1

$p(x) = {3x}^{2} - kx + 6$

I guess, 3 is the sum of the zeroes

By the general formulae,

ax²+bx+c = 0 then sum of roots is (-b/a)

In the given polynomial

p(x) = 3x²-kx+6 = 0

a = 3

b = -k

c = 6

Given, sum of roots = 3

$\frac{ - b}{a} = 3$

$\frac{ - ( - k)}{3} = 3 \\ k = 3 \times 3 \\ k = 9$

Answer 2

Answer:

$\begin{gathered}\sf \red{Poynomial \implies \: x + 3} \\ \sf \green{Factor\: of \: poynomial \implies \: {3x}^{2} + kx + 6}\end{gathered} </p><p>$

$\begin{gathered}\implies \sf{x + 3 = 0} \\ \implies \sf{x = 0 - 3} \\ \therefore \sf{x = - 3}\end{gathered}$

$\begin{gathered}\implies \sf \purple{ {3x}^{2} + kx + 6 = 0} \\ \implies \sf{ 3 \times ( - 3) \times ( - 3) + k( - 3) + 6 = 0} \\ \implies \sf{27 + ( - 3)k + 6 = 0} \\ \implies \sf{27 - 3k + 6 = 0} \\ \implies \sf{33 - 3k = 0} \\ \implies \sf{ - 3k = 0 - 33} \\ \implies \sf{ - 3k = - 33} \\ \implies \sf{k = \frac{33}{3} } \\ \sf \therefore \orange{k = 11}\end{gathered} </p><p></p><p> </p><p>$

$\star \: \bf \underline \pink{Verification : }$

$\begin{gathered}\implies \sf \purple{ {3x}^{2} + kx + 6 } \\ \implies \sf{ 3 \times ( - 3) \times ( - 3) + 11( - 3) + 6 } \\ \implies \sf{27 + ( - 3)11 + 6 } \\ \implies \sf{27 - 3k \times\:11 + 6 } \\ \implies \sf{33 - 3(11) } \\ \implies \sf{ 33-33} \\ \sf \therefore \orange{0}\end{gathered} </p><p>$

$\bf\green{Hence,verified}$