Question

6. Find a quadratic polynomial each with the given numbers as the sum and the product off its zeroes: 4,-2​

Answer 1

Step-by-step explanation:

Given -

• sum of zeroes = 4
• product of zeroes = -2

To Find -

• A quadratic polynomial

As we know that :-

• α + β = -b/a

→ 4/1 = -b/a ......... (i)

And

• αβ = c/a

→ -2/1 = c/a ...... (ii)

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

a = 1

b = -4

c = -2

As we know that :-

For a quadratic polynomial :-

• ax² + bx + c

→ (1)x² + (-4)x + (-2)

→ x² - 4x - 2

Hence,

The quadratic polynomial is x² - 4x - 2

Answer 2

${\huge{\underbrace{\overbrace{\red{Answer:-}}}}}$

$\large\underline\mathrm{The \: quadratic \: polynomial \: is \: x² \: - \: 4x \: - \: 2}$

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

• Sum of zeroes = 4
• Product of zeroes = -2

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

• A quadratic polynomial.

$\large\underline\mathrm{Solution}$

$\alpha \beta = - b \div a \\ \\ 4 \div 1 = - b \div a \: \: \: .....(1)$

And,

$\alpha \beta = c \div a \\ \\ - 2 \div 1 = c \div a \: \: .....(2)$

From (1) and (2), we get

$\large\underline\mathrm{From \: (1) \: and \: (2) \: , \: we \: get}$

$\implies$ a = 1

$\implies$ b = -4

$\implies$ c = -2

$\large\underline\mathrm{The \: quadratic \: polynomial:}$

$\implies$ ax² + bx + c

$\implies$ 1x² + (-4)x + (-2)

$\implies$ x² - 4x - 2

$\large\underline\mathrm{The \: quadratic \: polynomial \: is \: x² \: - \: 4x \: - \: 2}$

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