Question

1) Form a quadratic equation such that one of its roots is 5. Forma
quadratic equation for it and write. (For the formation of word
problem you can use quantities like age, rupees or natural numbers.)
(sample solution for the above example is given below students can
take another number to form another example)
Solution: We need one of the solutions of quadratic equation as 5. Then
we can take another root as any number like positive or negative number
or zero. Here I am taking another root of quadratic equation as 2.
Then we can form a word problem as below,
Smita is younger than her sister Mita by 3 years (5-2= 3). If the product
of their ages is (5 x 2 = 10). Then find their present ages. (to form a word
problem 1 mark)
Let the age of Mita be x,
Therefore age of Smita = x-3 (1 mark for this)
By the given condition,
X(x-3) = 10
X2 - 3x – 10 = 0 (to form a quadratic equation 1 mark)​

Answer 1

SOLUTION

TO DETERMINE

• Form a quadratic equation such that one of its roots is 5.

• Form a quadratic equation for it and write. (For the formation of word problem you can use quantities like age, rupees or natural numbers.)

EVALUATION

We have to form a quadratic equation such that one of its roots is 5

First we form the word problem as below :

Product of two consecutive natural numbers is 20 . Find the numbers

Formation of equation :

Let the consecutive natural numbers are x - 1 and x

So by the given condition

$\sf{x(x - 1) = 20}$

$\sf{ \implies {x}^{2} - x - 20 = 0}$

Which is the required Quadratic equation

Solve :

We now solve for x

$\sf{ {x}^{2} - x - 20 = 0}$

$\sf{ \implies {x}^{2} - 5 x + 4x - 20 = 0}$

$\sf{ \implies x(x - 5) + 4(x - 5)= 0}$

$\sf{ \implies (x - 5) (x + 4)= 0}$

x - 5 = gives x = 5

x + 4 = 0 gives x = - 4

So two roots are - 4 & 5

Thus one of the roots is 5

Find the number :

Since x is a natural number

$\sf{x \ne \: - 4}$

∴ x = 5

So the required numbers are 4 & 5

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Answer 2

Answer:

this is correct answer

Step-by-step explanation:

x2-3x-10=0