Find the roots of the following quadratic equations, if they exi
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    Quadratic Equations

    Multiple Choice QuestionsLong Answer Type

    21. Find two consecutive positive integers, sum of whose square is 365.
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    22. The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm. Find the other two sides.
    267 Views
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    Multiple Choice QuestionsShort Answer Type

    23. A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was Rs. 90. Find the number of articles produced and the cost of each article.
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    24. Find the roots of the following quadratic equations, if they exist by the method of completing the square:
    2x2 –7x + 3 = 0

    2x2 – 7x + 3 = 0
    rightwards double arrow     space space space space space straight x squared minus 7 over 2 straight x plus 3 over 2 equals 0 space space space space space space space left square bracket Dividing space by space 2 right square bracket
    rightwards double arrow space space space open curly brackets straight x squared minus 2. straight x.7 over 4 plus open parentheses 7 over 4 close parentheses squared close curly brackets minus open parentheses 7 over 4 close parentheses squared plus 3 over 2 equals 0

    rightwards double arrow         <pre>uncaught exception: <b>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</b><br /><br />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<br />#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>

    rightwards double arrow              <pre>uncaught exception: <b>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</b><br /><br />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<br />#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>

    rightwards double arrow                  open parentheses straight x minus 7 over 4 close parentheses squared space equals space 25 over 16

    rightwards double arrow              space space space space straight x minus 7 over 4 equals plus-or-minus 5 over 4

    rightwards double arrow               straight x equals 7 over 4 plus-or-minus 5 over 4 equals fraction numerator 7 plus 5 over denominator 4 end fraction comma space fraction numerator 7 minus 5 over denominator 4 end fraction

    rightwards double arrow             straight x equals 12 over 4 comma space 2 over 4 equals 3 comma space 1 half.

    Hence, the roots of the given quadratic equations are  3 and 1 half.
    213 Views
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    25. Find the roots of the following quadratic equations, if they exist by the method of completing the square:
    2 straight x squared plus straight x minus 4 space equals space 0
    117 Views
    Answer
    26. Find the roots of the following quadratic equations, if they exist by the method of completing the square:
    4 straight x squared plus 4 square root of 3 straight x plus 3 equals 0
    106 Views
    Answer
    27. Find the roots of the following quadratic equations, if they exist by the method of completing the square:
    2x2+x+ 4 = 0.
    135 Views
    Answer

    Multiple Choice QuestionsLong Answer Type

    28. Find the roots of the quadratic equations given in Q. 1, above by applying the quadratic formula.
    204 Views
    Answer
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    29. Find the roots of the factors of equations:
        straight x minus 1 over straight x equals 3 comma space space straight x not equal to 0.
    156 Views
    Answer
    30. The sum of the reciprocals of Rehman’s age (in years) 3 years ago and 5 years from now is space 1 third.
    Find his present age.
    182 Views
    Answer
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