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Polynomials

Long Answer Type

411. Find the zeroes of the quadratic polynomial x² – 5x + 6, and verify the relationship between the zeroes and the coefficients.

512 Views

412. Find the zeroes of x² –2 and verify the relationship between the zeroes and the coefficients.

280 Views

413. Find the zeroes of a quadratic polynomial 5x² – 4 – 8x and verify the relationship between the zeroes and the coefficients.

We have, 5x² – 8x – 4
= 5x² – 10x + 2x – 4
= 5x (x–2) + 2 (x – 2)
= (5x + 2) (x – 2)
So, the value of 5x² – 8x – 4 is zero when 5x + 2 = 0 or x – 2 = 0
i.e., when x = –2/5 or x = 2
Therefore, the zeroes of 5x² – 8x – 4 are –2/5 and 2.
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= $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$

Product of zeroes = $negative 2 over 5 cross times 2 equals fraction numerator negative 4 over denominator 5 end fraction$

= $fraction numerator Constant space term over denominator Coefficient space of space straight x squared end fraction.$

3113 Views

414. Find the zeroes of the following polynomial and verify the relationship between the zeroes and the coefficients

5 square root of 5 straight y squared plus 20 straight y plus 3 square root of 5

90 Views

415.

Verify that 3, -1, $fraction numerator negative 1 over denominator 3 end fraction$ are the zeroes of the cubic polynomial p(x) = 3x³ – 5x² –11x – 3 then verify the relationship between the zeroes and the coefficients.

2259 Views

416. Verify that the numbers given along side of the cubic polynomials below are their zeroes. Also verify the relationship between the zeroes and the coefficient in each case.
x³ – 4x² + 5x – 2, 2, 1, 1.

132 Views

417. Kind a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes as 2, -7, -14 respectively.

270 Views