Question

if x and B are the zeros of a polynomial such that X + Y is equal to 5 x b is equal to 4 then write the polynomial​

Answer 1

Step-by-step explanation:

Correct Question :-

• If α and β are the zeroes of a polynomial such that α + β = 5 and αβ = 4

Solution :-

Given -

α + β = 5

αβ = 4

To Find -

• Write the polynomial

As we know that :-

• α + β = -b/a

→ 5/1 = -b/a ...... (i)

And

• αβ = c/a

→ 4/1 = c/a ........ (ii)

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

a = 1

b = -5

c = 4

As we know that :-

For a quadratic polynomial :-

• ax² + bx + c

→ (1)x² + (-5)x + (4)

→ x² - 5x + 4

Hence,

The polynomial is x² - 5x + 4

Verification :-

• α + β = -b/a

→ 5 = -(-5)/1

→ 5 = 5

LHS = RHS

And

• αβ = c/a

→ -4 = -4/1

→ -4 = -4

LHS = RHS

Hence,

Verified...

It shows that our answer is absolutely correct.

Answer 2

$\large{\underline{\bf{\green{Given:-}}}}$

✰ sum of zeroes = 5

✰ product of zeroes = 4

$\large{\underline{\bf{\green{To\:Find:-}}}}$

✰ we need to find the polynomial

$\huge{\underline{\bf{\red{Solution:-}}}}$

let α and β are the zeroes of required polynomial.

So,

α + β = 5

αβ = 4

$: \implies \sf$p(x) = x² - (α + β)x + αβ

$: \implies \sf$x² -(5)x + 4

$: \implies \sf$x² - 5x +4 = 0

Hence the required polynomial is

⠀⠀⠀⠀=⠀x² - 5x +4 = 0

Now varification:-

α + β = - b/a

αβ = c/a

sum of zeroes :-

$: \implies \sf$5 = -(-5)/1

$: \implies \sf$5 = 5

Now product of zeroes:-

$: \implies \sf$4 =4/1

$: \implies \sf$ 4 = 4

LHS = RHS

hence varified.

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