Question

Find the polynomial whose sum and product of the zeros are 5 and -3 ( Hint : Use P(x) = x2 – (sum of the zeros)x + (product of the zeros)

Answer 1

AnsWer :

x² - 5x - 3.

GiveN :

• Sum of Zeros = 5.
• Product Of Zeros = - 3.

SolutioN :

* Sum of Zeros.

→ 5.

$\rule{90}2$

* Product Of Zeros.

→ - 3.

$\rule{90}2$

We have, Formula.

→ K[ x² -Sx + P ]

Where as,

• K Constant term.
• S Sum of Zeros.
• P Product of Zero.

Now,

→ K[ x² - ( 5 ) + ( - 3 ) ]

→ K [ x² - 5x - 3 ]

Therefore, the polynomial forms be x² - 5x - 3.

Answer 2

✯✯ QUESTION ✯✯

Find the polynomial whose sum and product of the zeros are 5 and -3 ( Hint : Use P(x) = x2 – (sum of the zeros)x + (product of the zeros)

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✰✰ ANSWER ✰✰

• Sum of Zeroes (α+β) = 5
• Product of Zeroes (αβ) = -3

➥Using Formula : -

$\implies\tt{\small{\boxed{\bold{\bold{\pink{\sf{{x}^{2}-(\alpha+\beta)x+(\alpha\beta)}}}}}}}$

➥Putting Values : -

$\implies\tt{{x}^{2}-(5)x+(-3)}$

$\implies\tt{{x}^{2}-5x-3}$

☛So , The quadratic polynomial is x²-5x-3...

_______________________

✔VERIFICATION : -

➮HERE : -

• a = 1
• b = -5
• c = -3

★Sum of Zeroes : -

$\implies\tt{5=\dfrac{(-b)}{a}}$

$\implies\tt{5=\dfrac{-(-5)}{1}}$

$\implies\tt{5=5}$

$\pink\longmapsto\:\large\underline{\boxed{\bf\red{L.H.S}\orange{=}\purple{R.H.S}}}$

★Product of Zeroes : -

$\implies\tt{-3=\dfrac{c}{a}}$

$\implies\tt{-3=\dfrac{-3}{1}}$

$\implies\tt{-3=-3}$

✺ HENCE VERIFIED ✺