Question

1.find the Quadratic polynomial the sum and product of whose zeroes are-3 and 2 respectively

2.find the mean of the following data
7, 6, 5, 0, 7, 8, 9


3.write the formula used to find the surface area of the sphere.

4.the sum of first 8 terms of an AP is 100 and sum of first 19 terms is 551.Find AP.​

Answer 1

1- x^2+3x+2=0

2- 42/7=6

3- Surface area of sphere- 4pi r^2

4- S8= n/2(2a+(n-1)d)=100
=8/2(2a+7d)=100
By solving this u will get,
8a+28d=100
Now divide it by 4
2a+7d=100

S19=19/2(2a+(19-1)d)=551
By solving this and dividing by 2 u will get,
19a+171d=551
And now multiply the first one with 19 and second one with 2
After multiplying solve it by elimination method you will get
a=2 and d=3
AP= 2,5,8.....

Answer 2

Question 1 : Find the Quadratic polynomial the sum and product of whose zeroes are -3 and 2 respectively.

Answer :

As given :

$\tt{\alpha + \beta = - 3}$

and

$\tt{\alpha \beta \: = 2}$

Now, as per the equation :

$\tt{x {}^{2} + ( \alpha + \beta )x + \alpha \beta = 0}$

The quadratic equation formed is :

$\tt{x {}^{2} - 3x + 2 = 0}$

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Question 2 : Find the mean of the following data :

7, 6, 5, 0, 7, 8, 9

Answer :

We know that,

$\tt{Mean = \frac{ sum \: of\: all \: numbers}{ total \: numbers}}$

$\tt{ = \frac{7 + 6 + 0 + 7 + 8 + 9}{7}}$

$\tt { = \frac{42}{7}}$

= 6

Mean of the data is 6.

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Question 3 : Write the formula used to find the surface area of the sphere.

Answer :

Formula of Surface area of sphere is :

$\tt{4 \pi r {}}^{2}$

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Question 4 : The sum of first 8 terms of an AP is 100 and sum of first 19 terms is 551. Find AP.

Answer :

Refer the attachment for the answer.

Hope it helps.

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