Question

If zeroes of the polynomial x² + 4x + 2a are α and 2/α , then the value of a is -

Answer 1

Answer:

a = 1

Solution:

Zeroes of polynomial x²+ 4x + 2a = α and 2/α

By comparing this polynomial with ax² + bx + c

• a = 1
• b = 4
• c = 2a

We know, product of zeroes of any polynomial is,

= c/a

= 2a/1

= 2a

Using given zeros,

→ α × 2/α = 2

Comparing the above Equations,

→ 2a = 2

→ a = 2/2 = 1

Therefore, the value of a is 1.

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If any polynomial is represented as ax² + bx + c, then

Sum of zeroes = -(Coefficient of x) / Coefficient of x² = -b/a

Product of zeroes = Constant term / Coefficient of x² = c/a

Answer 2

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Given ,

The zeroes of the polynomial x² + 4x + 2a are α and 2/α

We know that ,

Product of zeroes = c/a

Thus ,

➡2α/α = 2a/1

➡2a = 2

➡a = 1

Hence , the value of a is 1