Question

form a quadratic polynomial whose zeros are -2 and -1​

Answer 1

ANSWER:

• Quadratic polynomial = x²+3x+2

GIVEN:

• α = (-2)
• β = (-1)

TO FIND:

• Quadratic polynomial whose zeros are (-2) and (-1)

SOLUTION:

Quadratic polynomial when zeros are given:

$x {}^{2} - ( \alpha \: + \beta)x + \alpha \beta \: \: \: .....(i)$

Finding zum of zeros (α+β)

Here:

α= (-2)

β=(-1)

=> α+β = (-2)+(-1)

=> α+β = (-3)

Now finding product of zeros (αβ)

=> αβ = (-2)(-1)

=> αβ = 2

Putting the values in eq(i)

P(x) = x²-(-3)x+2

P(x) = x²+3x+2

Quadratic polynomial = x²+3x+2

NOTE:

some important formulas

$\implies \: \alpha \: + \beta \: = \dfrac{ - (coefficient \: of \: x)}{coefficient \: of \: x {}^{2} } \\ \\ \implies \: \alpha \: \beta \: = \dfrac{ constant \: term}{coefficient \: of \: x {}^{2} } \:$

Answer 2

Answer:

Given:

We have been given that the two zeroes of a quadratic polynomial are -2 and -1.

To find:

We need to find the quadratic polynomial.

Solution:

As the two zeroes of the polynomial are given that is α = -2 and β = -1.

So, the sum of zeroes α + β

= -2 + (-1)

= -2 -1

= -3______(1)

And the product of zeroes that is αβ

= -2 × (-1)

= 2______(2)

Inorder to find the polynomial, we have

x^2 - (α + β)x + αβ

Substituting the values from equation 1 and 2 we get,

= x^2 - (-3)x + 2

= x^2 + 3x + 2

Hence, the polynomial is x^2 + 3x + 2.