Question

if x² = -2 is root of the equations 3x² + 7x + p = 0 then find the value of p​

Answer 1

Answer:

p can be = 6 - 7$\sqrt{2}$i  or 6 + 7

Step-by-step explanation:

$x^2$ = -2

$x$ = $+/-$ $\sqrt{2}$i

hence, substituting this value in the given equation:

Case-1 (x = +$\sqrt{2}$i)

3x² + 7x + p = 0

3($\sqrt{2}$i)² + 7($\sqrt{2}$i ) = -p

3(-2) + 7$\sqrt{2}$i = -p

-6 + 7$\sqrt{2}$i = -p

p = 6 - 7$\sqrt{2}$i

Case-2 (x = -$\sqrt{2}$i)

3x² + 7x + p = 0

3(-$\sqrt{2}$i)² + 7(-$\sqrt{2}$i ) = -p

3(-2) - 7$\sqrt{2}$i = -p

-6 - 7$\sqrt{2}$i = -p

p = 6 + 7$\sqrt{2}$i