Question

POLYNOMIALS
1. Find a quadratic polynomial whose zeroes are 3 and -5
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Answer 1

FOR INDIANs {Grade 10 CBSE Boards}

[we are taught in another way in our schools for 10th grade]

Answer:

`p(x) = x^2 + 2x -15`

Explanation:

Let α = 3 and β= -5

Polynomial ⇒

`p(x) = k[x^2-(`α + β
`)x + (`αβ
`)]`

`p(x) = k[x^2 - (3-5) x+ (3(-5))]`

`p(x) = k[x^2 - (-2)x + (-15)]`

`p(x) = k[x^2 + 2x - 15]`

∴
`p(x) = x^2 + 2x -15` [where k = 1]

Answer 2

y = x² + 2x - 15

Explanation:

Given the zeros are x = 3 and x = - 5 then the factors are (x - 3) and (x + 5)

The polynomial is then the product of its factors, thus

y = (x - 3)(x + 5) ← expand using FOIL

y = x² + 2x - 15