Question

If α,β are the zeroes of the polynomial fx=2x2+5x+k satisfy the relation α2+β2+αβ=214 , then find the value of k.

Answer 1

Step-by-step explanation:

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Answer 2

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If α,β are the zeroes of the polynomial f ( x ) =2x2+5x+k satisfy the relation α²+β²+αβ=21/4 , then find the value of k.

Given:

α and β are the zeroes of the polynomial f ( x ) = 2x² + 5x + k.

• a = 2

• b = 5

• c = k

To find out:

Find the value of k ?

Solution:

★ Sum of zeroes:

α + β = - b / a

⇒ - 5 / 2

★ Product of zeroes:

α.β = c/a

⇒ k / 2

Now,

α² + β² + αβ = 21/4 [ Given ]

★ Adding and Subtracting αβ

⇒ ( α² + β² + αβ + αβ ) - αβ = 21/4

⇒ ( α² + β² + 2αβ ) - αβ = 21/4

We know that,

α² + β² + 2αβ = ( α + β )²

⇒ ( α + β )² - αβ = 21/4

⇒ ( -5/2 )² - k/2 = 21/4 [ α + β = -5/2 and αβ = k/2 ]

⇒ 25/4 - k/2 = 21/4

⇒ -k/2 = 21/4 - 25/4

⇒ -k/2 = -4/4

⇒ -k = -4/4 × 2

⇒ -k = -2

⇒ k = 2

Hence, the value of k is 2.