Question

If 7x^2 - (2p^2 - 8)x + 16 = 0 has 2 roots which are equal in magnitude but opposite in sign find p

Answer 1

7x² - (2P² - 8)x + 16 = 0 has two roots which are equal in magnitude but opposite in sign.

Let a and -a are two roots of given quadratic equation.

sum of roots = - coefficient of x/coefficient of x²

-a + a = -{-(2p² - 8)}/7

=> 0 = (2p² - 8)/7

=> 2p² - 8 = 0

=> P² = 4

=> p = ±2

hence, p = 2 or -2

Answer 2

HELLO DEAR,

GIVEN:-

7x² - (2P² - 8)x + 16 = 0 has two roots which are equal in magnitude but opposite in sign.

Let ß and -ß are two roots of given quadratic equation.

so, we know

sum of roots = - coefficient of x/coefficient of x²

here, cofficient of x = -(2p² - 8)

cofficient of x² = 7

-ß + ß = -{-(2p² - 8)}/7

0 = (2p² - 8)/7

2p² - 8 = 0

P² = 4

p = ±2

HENCE, p = 2 or -2

I HOPE ITS HELP YOU DEAR,

THANKS