Question

If the sum and product of the quadratic
polynomial are - 4 and -12, then the
quadratic polynomial is
A. x2 - 4x - 12
B. x2 + 4x + 12
C. x2 + 4x - 12
D. x2 + 4x - 11​

Answer 1

✬ Polynomial = x² + 4x – 12 ✬

Step-by-step explanation:

Given:

• Sum of zeros of quadratic polynomial is –4.
• Product of zeros of is –12.

To Find:

• What is the quadratic polynomial?

Solution: Let the zeros of quadratic polynomial be α & β. Therefore,

➟ Sum of zeros = α + β

➟ – 4 = α + β

and

➟ Product of zeros = α × β

➟ –12 = α × β

As we know that a quadratic polynomial whose zeros are α and β is given by

★ p(x) = { x² – (α + β)x + αβ } ★

$\implies{\rm }$ p(x) = {x² – (–4)x + (–12)}

$\implies{\rm }$ p(x) = {x² – (–4x) – 12}

$\implies{\rm }$ p(x) = x² + 4x – 12

Hence, the quadratic polynomial is x² + 4x – 12.

(Option C is correct)

[ Verification ]

Now finding the zeroes the quadratic polynomial by middle term splitting.

➮ x² + 4x – 12

➮ x² + 6x – 2x – 12

➮ x(x + 6) – 2 (x + 6)

➮ (x – 2) (x + 6)

➮ x – 2 = 0 or x + 6 = 0

➮ x = 2 or x = –6

So the zeros of polynomial are 2 and –6.

• Sum of zeros = –(Coefficient of x)/Coefficient of x²

• Product of zeros = Constant term/Coefficient of x²

Sum

2 + (–6)

2 – 6

4 = –(4)/1 = 4

Product

2 × –6

–12 = –12/1 = –12

$\large\bold{\texttt {Verified }}$

Answer 2

Answer:

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