Question

Which of the following is a quadratic polynomial whose sum and product respectively of the zeros are -8/3 and 4/3

Answer 1

Step-by-step explanation:

Given :-

• Sum of zeroes = -8/3
• Product of zeroes = 4/3

To Find -

• A quadratic polynomial

As we know that :-

• α + β = -b/a

⇝-8/3 = -b/a ..... (i)

And

• αβ = c/a

⇝4/3 = c/a .... (ii)

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

a = 3

b = 8

c = 4

As we know that :-

For a quadratic polynomial :-

• ax² + bx + c

⇝(3)x² + (8)x + 4

⇝3x² + 8x + 4

Hence,

The quadratic polynomial is 3x² + 8x + 4.

Answer 2

$\huge\underline\mathbb{\red Q\pink{U}\purple{ES} \blue{T} \orange{IO}\green{N :}}$

Find the quadratic polynomial whose sum of the zeroes is -8/3 and product of the zeroes is 4/3.

$\huge\underline\mathbb{\red S\pink{O}\purple{LU} \blue{T} \orange{IO}\green{N :}}$

★ Given that,

$\tt\: ↪ Sum \: of \: the \: zeroes : \alpha + \beta = \frac{-8}{3}$

$\tt\: ↪ Product \: of \: the \: zeroes : \alpha \beta = \frac{4}{3}$

★ We know that,

Form of the Quadratic Polynomial is :

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

• Substitute the zeroes.

$\sf\:⟹ x^{2} - (- \frac{8}{3})x + (\frac{4}{3}) = 0$

$\sf\:⟹ x^{2} + \frac{8}{3}x + \frac{4}{3} = 0$

$\sf\:⟹ \frac{3x^{2} + 8x + 4}{3} = 0$

$\sf\:⟹ 3x^{2} + 8x + 4 = 0 \times 3$

$\sf\:⟹ 3x^{2} + 8x + 4 = 0$

$\underline{\boxed{\bf{\purple{∴ Hence \: the \: Quadratic \: Polynomial \: is \: “ \: 3x^{2} + 8x + 4 = 0 \: ”}}}} </p><p>$