Find two numbers whose sum is 27 and product is 182 ?

byAmlesh Mahato •February 28, 2021

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Solution:

⇨Let one of the number be x

⇨ Then another number is = 27-x

A/Q

x(27-x)=182

$\large \Rightarrow x^{2}-27x+182= 0$

$Find two numbers whose sum is 27 and product is 182 ?$

$\large \Rightarrow x^{2}-27+182= 0$

$\large \Rightarrow x^{2}-(14+13)x+182= 0$

$\large \Rightarrow x^{2}-14x-13x+182= 0$

$\large \Rightarrow x(x-14)-13(x-14)=0$

$\large \Rightarrow (x-13)(x-14)=0$

$\large \Rightarrow x-13=0,x-14=0$

$\large \Rightarrow x=13,x=14$

Therefore the two numbers are = 13, 14

Exercise 4.2

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

(i) $x^2-3x-10=0$

(ii) $Find the roots of 2x^2+x-6=0 quadratic equations by factorization ?$

(iii) $Find the roots of \sqrt{2}x^2+7x+5\sqrt{2}=0 quadratic equations by factorization ?$

(iv) $Find the roots of 2x^2-x+\frac{1}{8}=0 quadratic equations by factorization ?$

(v) $\large 100x^{2}-20x+1=0$

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

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

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

6. 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 ` 90, find the number of articles produced and the cost of each article.

Tags: Chapter-4 Exercise-4.2 Math- Class 10

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