Page 2 - 10 Math Lesson Notes-Standard form, Ch-4

Ans: Let the breadth of plot be x m
then, length = 1 + 2x
It is given that, area = 528
length breadth = 528
x(1 + 2x) = 528
2
x + 2x = 528
2
2x + x - 528 = 0 is the required quadratic equation.

ii) James and John together have 35 marbles. Both of them lost 5 marbles
each, and the product of the number of marbles they now have is 126.

Ans: Let the number of marbles James had be x.
Then the number of marbles John had = 35 - x
The number of marbles left with James after losing 5 marbles = x - 5
The number of marbles left with John after losing 5 marbles = 35 - x - 5
=30 - x.
According to the given condition
(x - 5) (30 - x) = 126
2
30x - x - 150 + 5x = 126
2
-x + 35x - 276 = 0
2
x - 35x + 276 = 0 is the required equation.

iii) The sum of two numbers is 15 and the sum of their reciprocals is .

Formulate the quadratic equations to find the numbers.

Ans: Let the required numbers be x and (15 - x)
Then,

3x( 15 - x) = 150
2
3x - 45x + 150 = 0
2
x - 15x + 50 = 0 is the required equation.

iv) A two digit number is 5 times the sum of its digits and is also equal to 5 more
than twice the product of its digits. Formulate the quadratic equation to find
the number.
Ans: Let the digit at the ten's place be x and units place be y.
Then the number = 10x + y
According to the given conditions
10x + y = 5(x + y) (i)
10x + y = 5 + 2xy (ii)
(i) 10x + y = 5x + 5y

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