Question

Find a quadratic polynomial who's sum and product of zeroes are respectively
$a) \sqrt{5} \frac{1}{5} \\ b) 4 \: and \: 1 \\ c) - 1 \: and \: \frac{1}{4}$
​

Answer 1

•Step-by-step explanation

•To find: Quadratic Polynomial.

•where , ( α + β ) is sum of zeroes and αβ is product of zeroes.

•Here, α = - 4 and β = 2. ⇒ α + β = -4 + 2 = -2.

αβ = -4 × 2 = -8. ⇒ Quadratic •Polynomial = k ( x² - ( -2 ) x + ( -8 ) ) ...

°Therefore, Quadratic Polynomial is k ( x² + 2x - 8 )

Answer 2

Step-by-step explanation:

Given :-

Sum and product of zeroes are

• a) √5 and 1/5
• b) 4 and 1
• c) -1 and 1/4

To Find :-

• A quadratic polynomial

Now,

a)

Sum of zeroes = -b/a

→ √5/1 = -b/a

→ 5√5/5 = -b/a

And

product of zeroes = c/a

→ 1/5 = c/a ..... (ii)

Now, From (i) and (ii), we get :-

a = 5

b = -5√5

c = 1

As we know that :-

For a quadratic polynomial :-

• ax² + bx + c

→ (5)x² + (-5√5)x + 1

→ 5x² - 5√5x + 1

b)

Sum of zeroes = -b/a

→ 4/1 = -b/a ..... (i)

And

Product of zeroes = c/a

→ 1/1 = c/a ..... (ii)

Now,

From (i) and (ii), we get :-

a = 1

b = -4

c = 1

As we know that :-

For a quadratic polynomial :-

• ax² + bx + c

→ (1)x² + (-4)x + 1

→ x² - 4x + 1

c)

Sum of zeroes = -b/a

→ -1/1 = -b/a

→ -4/4 = -b/a ..... (i)

And

Product of zeroes = c/a

→ 1/4 = c/a ..... (ii)

Now, From (i) and (ii), we get :-

a = 4

b = 4

c = 1

As we know that :-

For a quadratic polynomial :-

• ax² + bx + c

→ (4)x² + (4)x + 1

→ 4x² + 4x + 1