{"id":1343,"date":"2022-03-03T07:09:37","date_gmt":"2022-03-03T07:09:37","guid":{"rendered":"https:\/\/mdr.foobrdigital.com\/?p=1343"},"modified":"2022-03-03T07:09:37","modified_gmt":"2022-03-03T07:09:37","slug":"roots-of-a-quadratic-equation","status":"publish","type":"post","link":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/2022\/03\/03\/roots-of-a-quadratic-equation\/","title":{"rendered":"Roots of a Quadratic Equation"},"content":{"rendered":"\n

The standard form of a quadratic equation is:<\/p>\n\n\n\n

ax2<\/sup> + bx + c = 0<\/code><\/pre>\n\n\n\n
Here, a<\/var>, b<\/var>, and c<\/var> are real numbers and a<\/var> can’t be equal to 0.<\/p>\n\n\n\n
We can calculate the root of a quadratic by using the formula:<\/p>\n\n\n\n
x = (-b \u00b1 \u221a(b2<\/sup>-4ac)) \/ (2a)<\/code><\/pre>\n\n\n\n
The \u00b1<\/code> sign indicates that there will be two roots:<\/p>\n\n\n\n
root1 = (-b + \u221a(b2<\/sup>-4ac)) \/ (2a)\nroot1 = (-b - \u221a(b2<\/sup>-4ac)) \/ (2a)<\/code><\/pre>\n\n\n\n
The term b2<\/sup>-4ac<\/code> is known as the determinant<\/strong> of a quadratic equation. It specifies the nature of roots. That is,<\/p>\n\n\n\n
  • if\u00a0determinant > 0<\/strong>, roots are real and different<\/li>
  • if\u00a0determinant == 0<\/strong>, roots are real and equal<\/li>
  • if\u00a0determinant < 0<\/strong>, roots are complex complex and different<\/li>
  • <\/li><\/ul>\n\n\n\n
    Java Program to Find Roots of a Quadratic Equation<\/h2>\n\n\n\n
    public class Main {\n\n  public static void main(String[] args) {\n\n    \/\/ value a, b, and c\n    double a = 2.3, b = 4, c = 5.6;\n    double root1, root2;\n\n    \/\/ calculate the determinant (b2<\/sup> - 4ac)\n    double determinant = b * b - 4 * a * c;\n\n    \/\/ check if determinant is greater than 0\n    if (determinant > 0) {\n\n      \/\/ two real and distinct roots\n      root1 = (-b + Math.sqrt(determinant)) \/ (2 * a);\n      root2 = (-b - Math.sqrt(determinant)) \/ (2 * a);\n\n      System.out.format(\"root1 = %.2f and root2 = %.2f\", root1, root2);\n    }\n\n    \/\/ check if determinant is equal to 0\n    else if (determinant == 0) {\n\n      \/\/ two real and equal roots\n      \/\/ determinant is equal to 0\n      \/\/ so -b + 0 == -b\n      root1 = root2 = -b \/ (2 * a);\n      System.out.format(\"root1 = root2 = %.2f;\", root1);\n    }\n\n    \/\/ if determinant is less than zero\n    else {\n\n      \/\/ roots are complex number and distinct\n      double real = -b \/ (2 * a);\n      double imaginary = Math.sqrt(-determinant) \/ (2 * a);\n      System.out.format(\"root1 = %.2f+%.2fi\", real, imaginary);\n      System.out.format(\"\\nroot2 = %.2f-%.2fi\", real, imaginary);\n    }\n  }\n}<\/code><\/pre>\n\n\n\n
    Output<\/strong><\/p>\n\n\n\n
    root1 = -0.87+1.30i and root2 = -0.87-1.30i<\/samp><\/code><\/pre>\n\n\n\n
    In the above program, the coefficients a<\/var>, b,<\/var> and c<\/var> are set to 2.3, 4, and 5.6 respectively. Then, the determinant<\/code> is calculated as b2<\/sup><\/code> - 4ac<\/code>.<\/p>\n\n\n\n
    Based on the value of the determinant, the roots are calculated as given in the formula above. Notice we’ve used library function Math.sqrt()<\/code> to calculate the square root of a number.<\/p>\n\n\n\n
    We have used the format()<\/code> method to print the calculated roots.<\/p>\n\n\n\n
    The format()<\/code> function can also be replaced by printf()<\/code> as:<\/p>\n\n\n\n
    System.out.printf(\"root1 = root2 = %.2f;\", root1);<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"
    The standard form of a quadratic equation is: Here, a, b, and c are real numbers and a can’t be equal to 0. We can calculate the root of a quadratic by using the formula: The \u00b1 sign indicates that there will be two roots: The term b2-4ac is known as the determinant of a quadratic equation. It specifies the nature of roots. That is, if\u00a0determinant > […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[350],"tags":[],"_links":{"self":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/1343"}],"collection":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/comments?post=1343"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/1343\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=1343"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=1343"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=1343"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}