Question

If 3x – 4 is a factor of the polynomial p(x) = 2x^3– 11x^2+kx – 20,
find the value k​

Answer 1

Answer:

$k = \frac{941}{36}$

Step-by-step explanation:

$g(x)=0 \\ </p><p>3x-4=0 \\ </p><p>3x=4 \\ </p><p>x=\frac{4}{3} \\ </p><p>p(x)=0 \\ </p><p>2x³-11x²+kx-20=0 \\ 2 \times { (\frac{4}{3}) }^{3} - 11 \times { (\frac{4}{3} )}^{2} + k \times \frac{4}{3} - 20 = 0 \\ 2 \times \frac{64}{27} - 11 \times \frac{16}{9} + \frac{4k}{3} - 20 = 0 \\ \frac{128}{27} - \frac{176}{9} + \frac{4k}{3} - 20 = 0 \\ \frac{127 - 528 + 36k - 540}{27} = 0 \\ 127 - 528 + 36k - 540 = 0 \times 27 \\ 127 - 528 + 36k - 540 = 0 \\ 127 - 528 - 540+ 36k = 0 \\ ( - 941) + 36k = 0 \\ 36k = 941 \\ k = \frac{941}{36}$