Question

3. Find the quadratic polynomial sum of whose zeroes is 2√5 and their product is

2​

Answer 1

Answer:

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Answer 2

Answer:

The required quadratic polynomial is x² - 2 √5 x + 2.

Step-by-step-explanation:

We have given that

Sum of zeroes = 2 √5

Product of zeroes = 2

We know that,

A quadratic polynomial P ( x ) is in the form of

P ( x ) = x² - ( Sum of zeroes ) x + ( Product of zeroes )

⇒ P ( x ) = x² - 2 √5 x + 2

∴ The required quadratic polynomial is x² - 2 √5 x + 2.

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Verification:

We have,

P ( x ) = x² - 2 √5 x + 2

Comparing with ax² + bx + c,

• a = 1
• b = - 2 √5
• c = 2

We know that,

Sum of zeroes = - b / a

⇒ 2 √5 = - ( - 2 √5 ) / 1

⇒ 2 √5 = 2 √5

∴ LHS = RHS

Also,

Product of zeroes = c / a

⇒ 2 = 2 / 1

⇒ 2 = 2

∴ LHS = RHS

Hence verified!