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Polynomials

Long Answer Type

431. If α, β are the zeroes of quadratic polynomial 2x² – 3x – 5, form a quadratic polynomial whose zeroes are α² and β².

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432. If α, β are the zeroes of quadratic poly-nomial x² – 3x + 2, form a quadratic polynomial whose roots are –α and –β.

161 Views

433. If α, β are the zeroes of quadratic polynomial x² – 3x – 1, form a quadratic polynomial whose roots are

1 over straight alpha squared comma space 1 over straight beta squared.

122 Views

434. Factorize 2x⁴ + x³ – 14x² – 19x – 6 by x² + 3x + 2 and verify the division algorithm.

163 Views

Short Answer Type

435. Find all the zeroes of the polynomial x³ + 3x² – 2x – 6, if two of its zeroes are – $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$

Since two zeroes are -

square root of 2 space and space square root of 2

= x² – 2 is a factor of the given polynomial.
Now, we divide the given polynomial by x²–2.
Since two zeroes are - = x2 – 2 is a factor of the given polynom

Hence, the zeroes of the given polynomial are

space space square root of 2. space square root of 2 space Ans. space

1188 Views

436. Find all the zeroes of the polynomial 2a³ + x² – 6x – 3, if two of its zeroes are -

square root of 3 space and space square root of 3.

230 Views

437. If the polynomial 6x⁴+8x³ + 17x² + 21x + 7 is divided by another polynomial 3x²+ 4x +1, the remainder comes out to be (ax + b), find a and b.

2132 Views

438. If the polynomial x³ + 2x³ + 8x² + 12x + 18 is divided by another polynomial x² + 5, the remainder comes out to be px + q. Find the values of p and q.

211 Views