Question

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Answer 1

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Answer 2

Answer:

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Step-by-step explanation:

Question - 01

Given:

sum of zeroes = 4

product of zeroes = 1

To Find:

Quadratic polynomial

Solution:

We know,

p(x) = x² - ( sum of zeroes )x + ( product of zeroes )

= p(x) = x² - (4)x + (1)

= p(x) = x² - 4x + 1

Question - 02

Given,

x + y = 5......(1)

x - y = 1.......(2)

Using Elimination method

x + y = 5

x - y = 1

——————

2x = 4

——————

So,

x = 2

Putting the value of x in eq...(1)

2 + y = 5

y = 5 - 2

y = 3

Hence,Value of x = 2 and value of y = 3.

Question - 03

Here, a = 3

d = 8 - 3

d = 5

First lets find which term is 253

Let a, = 253,

a + (n - 1) d = 253

Putting values

3+ (n - 1) x 5 = 253

5(n - 1) = 253 - 3

5(n-1) = 250

(n-1) = 250/5

n-1 = 50

n = 50 + 1

n = 51

We need to find 20th term from the last term

Last term 51st

Second last term 51-1= 50th

Third last term = 51- 2 = 49th

And so on

So, 20th from last term (51 - 19)nd term.

= 32nd term

So, we have to find a(32)

a(n) = a + (n - 1) d

Putting values

a(32) = 3 + (32 -1) x 5

= 3 + 31 x 5

= 3 + 155

= 158

So, 20th term from the last term of the given AP is 158.

Question - 04

2x² - 5x + 3 = 0

Using splitting the middle term method

2x² - 3x - 2x + 3 = 0

x (2x - 3) – 1 (2x - 3) = 0

(2x-3) (x - 1) = 0

i) 2x-3 = 0

2x = 3

x = 3/2

Hence x =

ii) x - 1 = 0

x = 1

3/2 and 1 are the roots of the equation.

Question - 05

2tan²45° + cos²30° - sin²60°

= 2(1)² + (√3/2)² - (√3/2)²

= 2 + 3/4 - 3/4

= 2

Hence the answer is 2.