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Q6.    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.

Let the number of articles produced in a day  The cost of production of each articles will be  Given the total production on that day was . Hence we have the equation; But, x cannot be negative as it is the number of articles. Therefore,  and the cost of each article  Hence, the number of articles is 6 and the cost of each article is Rs.15.

Q5.    The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.

Let the length of the base of the triangle be . Then, the altitude length will be: . Given if hypotenuse is . Applying the Pythagoras theorem; we get So,    Or   But, the length of the base cannot be negative.  Hence the base length will be . Therefore, we have Altitude length   and  Base length

Q4.    Find two consecutive positive integers, the sum of whose squares is 365.

Let the two consecutive integers be  Then the sum of squares is 365. . Hence, the two consecutive integers are .

Q3.    Find two numbers whose sum is 27 and product is 182.

Let two numbers be x and y. Then, their sum will be equal to 27 and the product equals 182.                                         ...............................(1)                                            .................................(2) From equation (2) we have:  Then putting the value of y in equation (1), we get Solving this equation: Hence, the two required numbers are .

Q2.    Solve the problems given in Example 1.

(i) $x^2-45x+324 = 0$

(ii) $x^2-55x+750 = 0$

From Example 1 we get: Equations: (i)  Solving by factorization method:  Given the quadratic equation:  Factorization gives,  Hence, the roots of the given quadratic equation are . Therefore, John and Jivanti have 36 and 9 marbles respectively in the beginning. (ii)  Solving by factorization method:  Given the quadratic equation:  Factorization gives,  Hence, the roots of the given...

Q1.    Find the roots of the following quadratic equations by factorisation:

(iv)    $2x^2 -x + \frac{1}{8} = 0$

Given the quadratic equation:  Solving the quadratic equations, we get Factorisation gives,  Hence, the roots of the given quadratic equation are  .

Q1.    Find the roots of the following quadratic equations by factorisation:

(v)    $100x^2 -20x +1 = 0$

Given the quadratic equation:  Factorisation gives,  Hence, the roots of the given quadratic equation are  .

Q1.    Find the roots of the following quadratic equations by factorisation:

(iii)    $\sqrt2x^2 + 7x + 5\sqrt2 = 0$

Given the quadratic equation:  Factorisation gives,  Hence, the roots of the given quadratic equation are  .

Q1.    Find the roots of the following quadratic equations by factorisation:

(ii)    $2x^2 + x - 6 = 0$

Given the quadratic equation:  Factorisation gives,  Hence, the roots of the given quadratic equation are  .

Q1.    Find the roots of the following quadratic equations by factorisation:

(i)    $x^2 - 3x - 10 =0$

Given the quadratic equation:  Factorisation gives,  Hence, the roots of the given quadratic equation are .
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