Question

write a quadratic polynomial with zero 1 and 3​

Answer 1

Step-by-step explanation:

Given -

• Zeroes are 1 and 3

To Find -

• A quadratic polynomial

As we know that :-

• α + β = -b/a

→ 1 + 3 = -b/a

→ 4/1 = -b/a .......... (i)

And

• αβ = c/a

→ 1 × 3 = c/a

→ 3/1 = c/a ........ (ii)

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

a = 1

b = -4

c = 3

And

As we know that :-

For a quadratic polynomial :-

• ax² + bx + c

→ 1x² + (-4)x + 3

→ x² - 4x + 3

Hence,

The quadratic polynomial is x² - 4x + 3

Verification :-

→ x² - 4x + 3

→ x² - x - 3x + 3

→ x(x - 1) - 3(x - 1)

→ (x - 3)(x - 1)

Zeroes are -

x - 3 = 0 and x - 1 = 0

• x = 3 and x = 1

Answer 2

$\huge \mathfrak\pink{Answer:-}$

$\large\underline\mathrm\pink{The \: quadratic \: polynomial \: is \: x² \: - \: 4x \: + \: 3.}$

$\large\underline\mathrm\pink{Given:-}$

• zeroes are 1 and 3

$\large\underline\mathrm\pink{To \: find}$

• A quadratic polynomial.

$\large\underline\mathrm\pink{Solution}$

• α + β = -b/a

$\implies$ 1 × 3 = c/a

$\implies$ 4/1 = -b/a. ...(1)

$\large\underline\mathrm\pink{and}$

$\implies$ αβ = c/a

$\implies$ 1 × 3 = c/a

$\implies$ 3/1 = c/a. ...(2)

$\implies$ a = 1

$\implies$ b = -4

$\implies$ c = 3

$\large\underline\mathrm\pink{Thus,}$

$\large\underline\mathrm\pink{A \: quadratic \: polynomial:}$

$\implies$ ax² + bx + c

$\implies$ 1x² + (-4)x + 3

$\implies$ x² - 4x + 3

$\large\underline\mathrm\pink{hence,}$

$\large\underline\mathrm\pink{The \: quadratic \: polynomial \: is \: x² \: - \: 4x \: + \: 3.}$

$\large\underline\mathrm\pink{Verify}$

$\implies$ x² - 4x + 3

$\implies$ x² - x - 3x + 3

$\implies$ x(x -1) - 3(x - 1)

$\implies$ (x - 1)(x - 3)

$\implies$ x - 1 = 0

$\implies$ x = 1

$\implies$ x - 3 = 0

$\implies$ x = 3

$\large\underline\mathrm\pink{Hope \: it \: helps \: you \: plz \: mark \: me \: brainlist}$