Question

Sum of zeroes is 1 and product of the zeroes is 1/2 what is the quadratic equation

Answer 1

Answer:

$\large{\underline{\boxed{\sf 2x^2 - 2x + 1}}}$

Step-by-step explanation:

Let the zeroes of the quadratic polynomial be α and β.

Given that -

Sum of zeroes = 1

⇒ α + β = 1

Product of zeroes = $\sf \dfrac{1}{2}$

⇒ αβ = $\sf \dfrac{1}{2}$

We know that,

The quadratic polynomial is given by -

⇒ x² - (α + β)x + αβ = 0

⇒ x² - 1x + $\sf \dfrac{1}{2} = 0$

⇒ $\sf \dfrac{2x^2 - 2x + 1}{2} = 0$

⇒ 2x² - 2x + 1 = 0

Hence, the required answer is

(2x² - 2x + 1).

Answer 2

$\huge\textbf{Answer:-}$

• Let α and β be the zeros of the given quadratic polygon:-

According to the given question:-

• 1 is equal to the sum of zeros

So,

$= > \alpha + \beta = 1$

$= > \alpha + \beta = \frac{1}{2}$

We know that:-

=> x² - (α + β)x + αβ = 0

$= > x {}^{2} - 1x + \frac{1}{2}=0$

$= > \frac{2x {}^{2} - 2x + 1 {}^{} }{2} = 0$

$= > 2x {}^{2} - 2x + 1 = 0$

Therefore, 2x² - 2x + 1 is the answer:-

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