Question

${2x}^{3} - {x}^{2} - 13x - 6$

Answer 1

Hiii friend,


P(X) = 2X³-X²-13X-6

Let Alpha , beta and gamma are the Zeros of the polynomial P(X). Such that,


Alpha + Beta = 0


Sum of zeros = -(Coefficient of X²/Coefficient of X³)

Alpha + Beta + Gamma = -(-1)/2

0 + Gamma = 1/2

Gamma = 1/2

And,

Product of zeros = -(Constant term/Coefficient of X³)

Alpha × Beta × Gamma = -(-6)/2

Alpha × Beta × 1/2 = 6/2

Alpha × Beta = 6×2/2 => 3

Alpah × -Alpha = 3

-Alpha² = 3

Alpha = (+-) ✓3

Alpha + Beta = 0

(+-)✓3 + Beta = 0

Beta = (+-) ✓3

Hence,

-✓3 , +✓3 and 1/2 are the zeros of the given polynomial.


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