Question

20.Find a quadratic polynomial, whose zeroes are -3 and 4?​

Answer 1

Answer:

The polynomial is x² – x – 12.

Step-by-step explanation:

Zeros of polynomial = –3 and 4

A polynomial is in the form of :

x² – (α + β)x + (αβ) where α and β are zeros of the polynomial.

★ α + β

$\longrightarrow$ (–3) + 4

$\longrightarrow$ 1

★ αβ

$\longrightarrow$ (–3) × 4

$\longrightarrow$ –12

Polynomial =

$\longrightarrow$ x² – (1)x + (–12)

$\longrightarrow$ x² – x – 12

Therefore, the polynomial is x² – x – 12.

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Check whether (–3) and 4 are zeros are x² – x – 12.

$\longrightarrow$ x² + 3x – 4x –12

$\longrightarrow$ x(x + 3) – 4(x + 3)

$\longrightarrow$ (x – 4)(x + 3)

Zeros =

$\longrightarrow$ x = 4

$\longrightarrow$ x = –3

Answer 2

Let zeros be $\alpha$ and $\beta$

$\rm\alpha=-3$

$\rm\beta=4$

Polynomial:-

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

$\\ \sf\longmapsto x^2-(-3+4)x+(-3)(4)=0$

$\\ \sf\longmapsto x^2-(1)x+(-12)=0$

$\\ \sf\longmapsto x^2-x-12=0$