Consider a polynomial p x - x -cos 36- x -cos 84- x -cos 156- Then the coefficient of x 2 isA- 0B- 1C- -5-1-4D- -5-1-4

The correct option is A 0Coefficient of x^2 = (cos 36^∘ + cos 84^∘ + cos 156^∘) = (cos 36^∘ + cos 84^∘ cos 24^∘) = (2 cos 60^∘ cos 24^∘ cos 24^∘) = (c ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Local Maxima

Consider a po...

Question

Consider a polynomial $p (x) = (x - c o s 36^{\circ}) (x - c o s 84^{\circ}) (x - c o s 156^{\circ})$ . Then the coefficient of $x^{2}$ is

\frac{\sqrt{5} + 1}{4}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{\sqrt{5} - 1}{4}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

Coefficient of $x^{2}$
$= - (c o s 36^{\circ} + c o s 84^{\circ} + c o s 156^{\circ}) = - (c o s 36^{\circ} + c o s 84^{\circ} - c o s 24^{\circ}) = - (2 c o s 60^{\circ} c o s 24^{\circ} - c o s 24^{\circ}) = - (c o s 24^{\circ} - c o s 24^{\circ}) = 0$

Suggest Corrections

Similar questions

Q. Consider the polynomial

P (x) = (x - cos 36^{\circ}) (x - cos 84^{\circ}) (x - cos 156^{\circ})

, then coefficient of

x^{2}

Q. The degree of the polynomial

5 x^{2} + x^{4} + 5

The value of polynomial p(x) = x³ – x² + x + 1 at x = 1 is

Q. The number of polynomials

p (x)

satisfying

(p (x))^{2} = 1 + x p (x + 1)

for all real values of

x

Q. Number of value(s) of

x

which disobey(s) the condition

{log}_{3} (2 x^{2} + 6 x - 5) > 1, x \in N

Join BYJU'S Learning Program

Consider a polynomial p(x)=(x−cos 36∘)(x−cos 84∘)(x−cos 156∘). Then the coefficient of x2 is

Coefficient of x2 =−(cos 36∘+cos 84∘+cos 156∘)=−(cos 36∘+cos 84∘−cos 24∘)=−(2 cos 60∘ cos 24∘−cos 24∘)=−(cos 24∘−cos 24∘)=0

Consider a polynomial $p (x) = (x - c o s 36^{\circ}) (x - c o s 84^{\circ}) (x - c o s 156^{\circ})$ . Then the coefficient of $x^{2}$ is

Coefficient of $x^{2}$
$= - (c o s 36^{\circ} + c o s 84^{\circ} + c o s 156^{\circ}) = - (c o s 36^{\circ} + c o s 84^{\circ} - c o s 24^{\circ}) = - (2 c o s 60^{\circ} c o s 24^{\circ} - c o s 24^{\circ}) = - (c o s 24^{\circ} - c o s 24^{\circ}) = 0$