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Polynomials

Short Answer Type

331.

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

t² - 15

919 Views

332. Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

3 straight x squared minus straight x minus 4.

167 Views

333. Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

space 1 fourth comma space minus 1

170 Views

334. Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

square root of 2 comma space 1 third

684 Views

335. Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

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249 Views

336. Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
1, 1

274 Views

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

Let the quadratic polynomial be ax² + bx + c, and its zeroes be α and β. Then,

space space space straight alpha plus straight beta equals negative 1 fourth space rightwards double arrow space fraction numerator negative straight b over denominator straight a end fraction equals negative 1 fourth space rightwards double arrow space straight b space equals space minus 1 fourth straight a

and

αβ equals 1 fourth space rightwards double arrow space straight c over straight a equals 1 fourth space rightwards double arrow space straight c equals 1 fourth straight a

straight a equals 1 comma space

then

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So, quadratic polynomial which fits the given condition is

straight x squared plus 1 fourth straight x plus 1 fourth space space or space 4 straight x squared plus straight x plus 1.

266 Views

338. Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
4, 1

163 Views

339. Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:
p(x) = x³ – 3x² + 5x – 3, g(x) = x²– 2

172 Views

340. Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:
p(x) = x⁴ – 3x² + 4x + 5, g(x) = x² + 1 – x

128 Views