Question

Sum and product of zeros of a quadratic polynomial are 4 and -4 respectively. Find the polynomial.

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Answer 1

Step-by-step explanation:

quadratic polynomial can be written as

x^2 - ( sum of root) x + product of root

Answer 2

Let α and β are zeros of required quadratic polynomial.

$\sf \longrightarrow \alpha + \beta = 4 - - - - (given)$

$\sf \longrightarrow \alpha \beta = 1 - - - - (given)$

The required polynomial,

$\sf \longrightarrow {x}^{2} - ( \alpha + \beta )x + ( \alpha \beta ) = 0$

Now, using (1) and (2)

$\sf \longrightarrow {x}^{2} - 4x + 1 = 0$

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