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Q . 1 all parts
Answers
It's to easy bhai, all answer is
1. Find the roots of the following Quadratic Equations by factorization.
(i)
(ii)
(iii)
(iv)
(v)
Ans. (i)x2 − 3x – 10 = 0
⇒
⇒x (x − 5) + 2 (x − 5) = 0
⇒(x − 5) (x + 2) = 0
⇒x = 5, −2
(ii)
⇒
⇒2x (x + 2) – 3 (x + 2) = 0
⇒(2x − 3) (x + 2) = 0
⇒x =
(iii)
⇒
⇒
⇒
⇒
⇒
⇒
(iv)
= 0
⇒
⇒
⇒
⇒4x (4x − 1) – 1 (4x − 1) = 0
⇒(4x − 1) (4x − 1) = 0
⇒
(v)
⇒
⇒10x (10x − 1) – 1 (10x − 1) = 0
⇒(10x − 1) (10x − 1) = 0
⇒x =
5.The altitude of right triangle is 7 cm less than its base. If, hypotenuse is 13 cm. Find the other two sides.
Ans. Let base of triangle be x cm and let altitude of triangle be (x − 7) cm
It is given that hypotenuse of triangle is 13 cm
According to Pythagoras Theorem,
=
⇒
⇒169 =
⇒
= 0
Dividing equation by 2
⇒
⇒
⇒x (x − 12) + 5 (x − 12) = 0
⇒(x − 12) (x + 5)
⇒x = −5, 12
We discard x = −5 because length of side of triangle cannot be negative.
Therefore, base of triangle = 12 cm
Altitude of triangle = (x − 7) = 12 – 7 = 5 cm
6. A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that 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.
Ans. Let cost of production of each article be Rs x
We are given total cost of production on that particular day = Rs 90
Therefore, total number of articles produced that day = 90/x
According to the given conditions,
⇒
⇒
⇒
⇒
⇒
⇒x (x − 15) + 12 (x − 15) = 0
⇒(x − 15) (x + 12) = 0⇒x = 15, −12
Cost cannot be in negative, therefore, we discard x = −12
Therefore, x = Rs 15 which is the cost of production of each article.
Number of articles produced on that particular day =
= 6
bhai rs Aggarwal ka ch 4 ka ex 1 Bana. Aise m to tu math m fail kr jaega.
