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Sia ? 6 years, 3 months ago
Two zeros are {tex}2\pm\sqrt3{/tex}
Sum of Zeroes {tex}2 + \sqrt { 3 } + 2 - \sqrt { 3 } = 4{/tex}
and product of zeroes = {tex}( 2 + \sqrt { 3 } ) ( 2 - \sqrt { 3 } ) = 4 - 3 = 1{/tex}
Hence quadratic polynomial formed out of this will be a factor of given polynomial,
So, x2 - (sum of zeroes)x + product of zeroes
= x2 - 4x + 1 will be a factor of given polynomial,
Divide given polynomial with x2 - 4x + 1 to get other zeroes.

Now,
x2 -2x - 35
= x2 - 7x + 5x - 35
= x(x - 7) + 5(x - 7)
= (x - 5) (x - 7)
{tex}\therefore {/tex} Zeros are
x = 7 and x = -5
{tex}\therefore {/tex} Other two zeros are 7 and -5
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Posted by Muskan Chhilar 6 years, 3 months ago
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Sia ? 6 years, 3 months ago
The value of cos 105o + sin 105o is {tex}\frac{1}{\sqrt{2}}{/tex}
Cos trigonometric values are positive in “first and fourth” quadrants in coordinate axes.
Sin trigonometric values are positive in “first and second” quadrants in coordinate axes.
cos 105o + sin 105o = cos (90o + 15o) + sin (90o + 15o)
= - sin (15o) + cos (15o) (ascos (90o + {tex}\theta{/tex}) = - sin {tex}\theta{/tex} and sin (90o + {tex}\theta{/tex}) = cos {tex}\theta{/tex})
= cos 15o - sin 15o
{tex}\left.=\sqrt{2}\left[\frac{1}{\sqrt{2}} \cos 15^{\circ}-\frac{1}{\sqrt{2}} \sin 15^{\circ}\right] \quad \text { (Multiply and divide by } \sqrt{2}\right){/tex}
{tex}=\sqrt{2}\left[\sin 45^{\circ} \cos 15^{\circ}-\cos 45^{\circ} \sin 15^{\circ}\right] \quad\left(A s \sin 45^{\circ}=\cos 45^{\circ}=\frac{1}{\sqrt{2}}\right){/tex}
{tex}=\sqrt{2}\left[\sin \left(45^{\circ}-15^{\circ}\right)\right] \quad(A \sin (A-B)=\sin A \cos B-\cos A \sin B){/tex}
{tex}=\sqrt{2}\left[\sin 30^{\circ}\right]{/tex}
{tex}=\sqrt{2} \times \frac{1}{2}=\frac{1}{\sqrt{2}}{/tex}
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You can check NCERT Solutions here : https://mycbseguide.com/ncert-solutions.html
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