Question

Find all the zeroes of the polynomial
$2 {x}^{4} - 2 {x}^{3} - 7 {x}^{2} + 3x + 6$
if its two zeroes are
$- \sqrt{ \frac{3}{2} } \: \: and \: \: \sqrt{ \frac{3}{2} }$
want even steps please

Answer 1

Hiii Friend,

-✓3/2 and ✓3/2 are the Zeros of the polynomial 2X⁴-2X³-7X²+3X+6

(X+✓3/2) ( X-✓3/2) = X²-(✓3/✓2)² = X²-3/2 = 2X²-3/2 .

Consequently , (2X²-3) is a factor of P(X)

P(X) = 2X⁴-2X³-7X²+3X+6

G(X) = 2X²-3

On dividing P(X) by G(X) we get,

Reminder = 0

Quotient = X²-X-2

Factories the Quotient then we will get the two other zeros of P(X).


=> X²-X-2

=> X²-2X+X-2

=> X(X-2) +1(X-2)

=> (X-2) (X+1)

=> (X-2) = 0 OR (X+1) = 0

=> X = 2 OR X = -1


Hence,

2 , -1 , ✓3/2 and -✓3/2 are the four zeros of the polynomial 2X⁴-2X³-7X²+3X+6.



HOPE IT WILL HELP YOU...... :-)