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.
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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
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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
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    Answer
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    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

    4 straight x squared plus 4 square root of 3 straight x plus 3 equals 0 rightwards double arrow space space space open curly brackets left parenthesis 2 straight x right parenthesis squared plus 2. left parenthesis 2 straight x right parenthesis. square root of 3 plus left parenthesis square root of 3 right parenthesis squared close curly brackets space equals space 0 rightwards double arrow space space space space space space space space left parenthesis 2 straight x plus square root of 3 right parenthesis squared space equals space 0
    rightwards double arrow              2 straight x plus square root of 3 space equals space 0
    rightwards double arrow                       straight x equals negative fraction numerator square root of 3 over denominator 2 end fraction.
    So, this root is repeated twice.
    Hence, both the roots of the given equations are open parentheses negative fraction numerator square root of 3 over denominator 2 end fraction close parentheses.
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    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.
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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.
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    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.
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