Question

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Answer 1

Answer:

1st option:

Given: 2 is the root of

$f(x) = {3x}^{2} + px - 8$

$g(x) = {4x}^{2} - 2px + k$

has equal roots

To find: k

Solution:

2 is the root so f(2) = 0

$f(2) = {3(2)}^{2} + p(2) - 8 \\ 0 = 12 + 2p - 8 \\ 0 = 4 + 2p \\ p = - 2$

Substitute p in g(x),

${4x}^{2} - 2( - 2)x + k = 0 \\ {4x}^{2} + 4x + k = 0$

Since it has equal roots,

$d = {b}^{2} - 4ac = 0 \\ 0= {4}^{2} - 4(4)(k) \\ 0 = 16 - 16k \\ k = 1$

The value of k=1