Are you lagging in solving the nature of roots of the quadratic equation? If your answer is yes, then don’t get tensed we are here to help you to find the Nature of roots of a quadratic equation in simple techniques. Acquire the math skills to solve the algebraic problems with the help of a Worksheet on Nature of the Roots of a Quadratic Equation with answers. We can solve the nature of the roots by determining the discriminant D (\u0394) = b\u00b2 – 4ac<\/p>\n
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Let us discuss in detail the nature of the roots of a quadratic equation<\/a> with some examples.<\/p>\n Example 1.<\/strong> D = b\u00b2 – 4ac Example 2.<\/strong> The standard form of the quadratic equation is x\u00b2 – (sum of the roots) + (product of the roots) = 0 Example 3.<\/strong> The standard form of the quadratic equation is x\u00b2 – (sum of the roots) + (product of the roots) = 0 Example 4.<\/strong> D = b\u00b2 – 4ac Example 5.<\/strong> D = b\u00b2 – 4ac Example 6.<\/strong> We can find the nature of the roots by using the discriminant formula. Example 7.<\/strong> We can find the nature of the roots by using the discriminant formula. Example 8.<\/strong> We can find the nature of the roots by using the discriminant formula. Example 9.<\/strong> We can find the nature of the roots by using the discriminant formula. Example 10.<\/strong> We know that the imaginary roots always occur in pairs, so the other root is 5 + 2i. Are you lagging in solving the nature of roots of the quadratic equation? If your answer is yes, then don’t get tensed we are here to help you to find the Nature of roots of a quadratic equation in simple techniques. Acquire the math skills to solve the algebraic problems with the help of a … Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/142919"}],"collection":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/comments?post=142919"}],"version-history":[{"count":1,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/142919\/revisions"}],"predecessor-version":[{"id":142923,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/142919\/revisions\/142923"}],"wp:attachment":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media?parent=142919"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/categories?post=142919"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/tags?post=142919"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\nFind the discriminant and nature of roots of the quadratic equation x\u00b2 – 6x + 9 = 0.<\/p>\nSolution:<\/summary>\n
\na = 1, b = -6, c = 9
\n= (-6)\u00b2 – 4(1)(9)
\n= 36 – 36
\n= 0
\nD = 0
\nThus the roots are real, rational and equal.<\/p>\n<\/details>\n
\n
\nWhat is the sum and product of the Roots if the Quadratic Equation is x\u00b2 – 5x + 6 = 0.<\/p>\nSolution:<\/summary>\n
\nSubstitute the values in the equation
\nSum of the roots = -b\/a = -(-5)\/1 = 5\/1 = 5
\nProduct of the roots = c\/a = 6\/1 = 6
\nThus the sum and product of the roots of the given quadratic equation are 5 and 6.<\/p>\n<\/details>\n
\n
\nIf the Quadratic Equation is x\u00b2 + 9x + 20 what will be the sum of the Roots and product of the Roots?<\/p>\nSolution:<\/summary>\n
\nSubstitute the values in the equation
\nSum of the roots = -b\/a = -(9)\/1 = -9\/1 = -9
\nProduct of the roots = c\/a = 20\/1 = 20
\nThus the sum and product of the roots of the given quadratic equation are -9 and 20.<\/p>\n<\/details>\n
\n
\nDetermine the discriminant and nature of roots of the quadratic equation x\u00b2 – 4x + 3 = 0.<\/p>\nSolution:<\/summary>\n
\na = 1, b = -4, c = 3
\n= (-4)\u00b2 – 4(1)(3)
\n= 16 – 12
\n= 4
\nD = 4
\nThus the roots of the equation are real, rational, and unequal<\/p>\n<\/details>\n
\n
\nFind the discriminant and nature of roots of the quadratic equation x\u00b2 – 7x – 4 = 0.<\/p>\nSolution:<\/summary>\n
\na = 1, b = -7, c = -4
\n= (-7)\u00b2 – 4(1)(-4)
\n= 49 + 16
\n= 65
\nD = 65
\nThus the roots of the equation are real, irrational, and unequal<\/p>\n<\/details>\n
\n
\nFind the nature of the roots using the discriminant x\u00b2 + 4x + 4 = 0<\/p>\nSolution:<\/summary>\n
\nD = b\u00b2 – 4ac
\na = 1, b = 4, c = 4
\n= (4)\u00b2 – 4(1)(4)
\n= 16 – 16
\nD = 0
\nThus the roots of the equation are real, rational, and equal<\/p>\n<\/details>\n
\n
\nFind the nature of the roots using the discriminant 2x\u00b2 + 3x + 5 = 0<\/p>\nSolution:<\/summary>\n
\nD = b\u00b2 – 4ac
\na = 2, b = 3, c = 5
\n= (3)\u00b2 – 4(2)(5)
\n= 9 – 40
\nD = -31
\nThus the roots of the equation are non-real, imaginary<\/p>\n<\/details>\n
\n
\nFind the nature of the roots using the discriminant 3k\u00b2 + 7k + 8 = 0<\/p>\nSolution:<\/summary>\n
\nD = b\u00b2 – 4ac
\na = 3, b = 7, c = 8
\n= (7)\u00b2 – 4(3)(8)
\n= 49 – 96
\nD = -47
\nThus the roots of the equation are non-real, imaginary<\/p>\n<\/details>\n
\n
\nUsing the discriminant determines the nature of roots of the quadratic equation 9m\u00b2 – 6m + 1 = 0<\/p>\nSolution:<\/summary>\n
\nD = b\u00b2 – 4ac
\na = 9, b = -6, c = 1
\n= (-6)\u00b2 – 4(9)(1)
\n= 36 – 36
\nD = 0
\nThus the roots of the equation are real, rational, and equal.<\/p>\n<\/details>\n
\n
\nForm a quadratic equation with real coefficients when one of its roots is (5 \u2013 2i).<\/p>\nSolution:<\/summary>\n
\nThus, by getting the sum and product of the roots, we can form the needed quadratic equation.
\nThe sum of the roots = (5 + 2i) + (5 – 2i) = 10
\nThe product of the roots = (5 + 2i)(5 – 2i) = 25 + 4 = 29
\nThe standard form of the quadratic equation is x\u00b2 – (sum of the roots) + (product of the roots) = 0
\nx\u00b2 – 10x + 29 = 0 is the required quadratic equation.<\/p>\n<\/details>\n
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