Question

29. The quadratic polynomial whose sum of zeroes is 3 and product of zeroes is –2 is :

(1 Point)​

Answer 1

Step-by-step explanation:

Given -

• sum of zeroes = 3
• product of zeroes = -2

To Find -

• A quadratic polynomial

Now,

As we know that :-

• α + β = -b/a

→ 3/1 = -b/a ....... (i)

And

• αβ = c/a

→ -2/1 = c/a ....... (ii)

Now, from (i) and (ii), we get :

a = 1

b = -3

c = -2

As we know that :-

For a quadratic polynomial :-

• ax² + bx + c

→ (1)x² + (-3)x + (-2)

→ x² - 3x - 2

Hence,

The quadratic polynomial is x² - 3x - 2

Verification :-

As we know that :-

• α + β = -b/a

→ 3 = -(-3)/1

→ 3 = 3

LHS = RHS

And

• αβ = c/a

→ -2 = -2/1

→ -2 = -2

LHS = RHS

Hence,

Verified...

Answer 2

GIVEN

The quadratic polynomial whose sum of zeroes is 3 and product of zeroes is –2

TO FIND

Find the quadratic polynomial

SOLUTION

★Let the polynomial be ax² + bx + c and its zeros be α and β

Then α + β = 3 = -b/a

And

→ αβ = -2 = c/a

If a = 1 then b = -3 and c = -2

So, quadratic polynomial is x² - 3x - 2