Question

$\huge\bold{Question:-}$

★ Find a quadratic polynomial with zeroes 2 and 3.
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Answer 1

Step-by-step explanation:

Given -

• Zeroes are 2 and 3

To Find -

• A quadratic polynomial

As we know that :-

• α + β = -b/a

→ 2 + 3 = -b/a

→ 5/1 = -b/a ....... (i)

And

• αβ = c/a

→ 2×3 = c/a

→ 6/1 = c/a ........ (ii)

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

a = 1

b = -5

c = 6

For a quadratic polynomial :-

• ax² + bx + c

→ (1)x² + (-5)x + (6)

→ x² - 5x + 6

Hence,

The quadratic polynomial is x² - 5x + 6

Answer 2

[HeY Mate]

$\huge\bold\red{Answer}$

Given

• Zeroes of polynomial = 2 and 3.

To Find

• Polynomial = ?

Formula of polynomial = x²(α+β)x+αβ=0

Where,

$</u></strong><strong><u> </u></strong><strong><u>\</u></strong><strong><u>t</u></strong><strong><u>t</u></strong><strong><u> </u></strong><strong><u>\</u></strong><strong><u>i</u></strong><strong><u>m</u></strong><strong><u>p</u></strong><strong><u>l</u></strong><strong><u>i</u></strong><strong><u>e</u></strong><strong><u>s</u></strong><strong><u> </u></strong><strong><u>\alpha = 2 \\ </u></strong><strong><u>\</u></strong><strong><u>t</u></strong><strong><u>t</u></strong><strong><u> </u></strong><strong><u>\</u></strong><strong><u>i</u></strong><strong><u>m</u></strong><strong><u>p</u></strong><strong><u>l</u></strong><strong><u>i</u></strong><strong><u>e</u></strong><strong><u>s</u></strong><strong><u> \beta = 3$

Solution:

$\tt \implies \: polynomial = x {}^{2} + ( \alpha + \beta ) + \alpha \beta \\ \tt \implies \: x {}^{2} + (2 + 3)x + 2(3)$

$\large \implies \boxed {\boxed {\tt \blue {x {}^2 + 5x + 6 }}}$

I Hope It Helps You✌️