α and β are the zeros of a polynomial, such that α+β=6 and αβ=4. Identify the polynomial. A x 2 −6x+4 B a 2 +6a+4 C p 2 +6p−4 D m 2 −6m−4

Question

$α$ and $β$ are the zeros of a polynomial, such that $α + β = 6$ and $α β = 4$ . Identify the polynomial.

A

$x^{2} - 6 x + 4$

B

$a^{2} + 6 a + 4$

C

$p^{2} + 6 p - 4$

D

$m^{2} - 6 m - 4$

Easy

Solution

Verified by GMS

We can also write $p (x)$ in this form also
$p (x) = x^{2} - \frac{- b}{a} x + \frac{c}{a}$

$\Rightarrow p (x) = x^{2} - (α + β) x + α β$
Now given that $α + β = 6$ and $α β = 4$
Substituting these values we get
$p (x) = x^{2} - (6) x + 4$ is the required polynomial.

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