Question

A polynomial whose sum and product of zeroes are – 4 and 3 is
[a]x2 + 4x +3

[b]x2 - 4x + 3

[c]none of these

[d]x2 - 4x - 3

Answer 1

Answer:

option a is correct answer.

Step-by-step explanation:

The standard form of qudratic polynomial is x^2-(alpha + betta)x+(alpha*betta)

x^2-(-4)x+(3)

x^2+4x+3

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Answer 2

Given:

Sum of zeroes = -4

and, product of zeroes = 3

To Find:

A quadratic polynomial ?

Solution:

As we know that :-

For a quadratic polynomial :

x² - (sum of zeroes)x + (product of zeroes)

→ x² - (-4)x + 3

→ x² + 4x + 3

Hence,

The polynomial is x² + 4x + 3

So, Option ( a ) x² + 4x + 3 is correct.

Verification :-

→ x² + 4x + 3

→ x² + x + 3x + 3

→ x(x + 1) + 3(x + 1)

→ (x + 3)(x + 1)

Zeroes are -

→ x + 3 = 0 and x + 1 = 0

→ x = -3 and x = -1

As Given -

• sum of zeroes = -4

→ -3 + (-1) = -4

→ -3 - 1 = -4

→ -4 = -4

LHS = RHS

• Product of zeroes = 3

→ -3 × -1 = 3

→ 3 = 3

LHS = RHS

Verified .