Question

if the zero of the polynomial is 3x2-px+2 and 4x2-qx-10 is 2,find the valu of 2p-3q

Answer 1

=14-9=5... Mark in Brainliest.plz

Answer 2

$Let \: p(x) = 3x^{2} - px + 2 \:and \\g(x) = 4x^{2} - qx - 10$

$Given \: 2 \:is \:the \:zero \:of \:p(x) \:and \:g(x)$

$\blue {( By \: Remainder \: Theorem )}$

$i ) p(2) = 0$

$3 \times 2^{2} - p \times 2 + 2 = 0$

$\implies 12 - 2p + 2 = 0$

$\implies 14 - 2p = 0$

$\implies - 2p = -14$

$\implies p = \frac{-14}{-2}$

$\implies p = 7 \: ---(1)$

$and \: ii ) g(2) = 0$

$4 \times 2^{2} - q\times 2 - 10= 0$

$\implies 16 - 2q -10 = 0$

$\implies 6 - 2q = 0$

$\implies - 2q = -6$

$\implies q = \frac{-6}{-2}$

$\implies q = 3 \: ---(2)$

$\implies Value \: 2p - 3q \\= 2 \times 7 - 3 \times 3\\= 14 - 9 \\= 5$

Therefore.,

$\red {Value \: 2p - 3q} \green {= 5}$

•••♪