Question

the zero of the quadratic polynomial x2+4x+k are alpha and bita find the value of k if 5 alph +2 bita =1

Answer 1

x2-5x+k

Here, a=1, b=-5 and c=k  

Now, α+ β = -b/a= -(-5)/1= 5  

α*β  = c/a= k/7= k

Now,α - β =1

Squaring both sides, we get,

(α - β)2=12  

⇒ α2 + β2 - 2αβ = 1

⇒ (α2 + β2 + 2αβ) - 4αβ = 1

⇒ (α +β)2 -4αβ =1

⇒ (5)2-4k=1

⇒ -4k= 7-25

⇒ -4k= -24  

⇒ k=6 So the value of k is 6.

hope you understood dude

Answer 2

Answer:

k = -21

Note:

If α and ß are the zeros of a quadratic polynomial Ax² + Bx + C , then ;

Sum of zeros , (α + ß) = -B/A

Product of zeros , αß = C/A

Solution:

Here,

The given quadratic polynomial is :

x² + 4x + k .

Clearly,

A = 1

B = 4

C = k

Also,

It is given that , α and ß are the zeros of the given quadratic polynomial .

Thus,

Sum of zeros = -B/A

=> α + ß = -4/1

=> α = - ß - 4 ------(1)

Also,

It is given that ;

5α + 2ß = 1 -------(2)

Now,

Putting α = - ß - 4 in eq-(2) , we get ;

=> 5α + 2ß = 1

=> 5(- ß - 4) + 2ß = 1

=> - 5ß - 20 + 2ß = 1

=> - 5ß + 2ß = 1 + 20

=> - 3ß = 21

=> ß = 21/-3

=> ß = -7

Now,

Putting ß = -7 in eq-(1) , we get ;

=> α = - ß - 4

=> α = - ( -7) - 4

=> α = 7 - 4

=> α = 3

Now,

Product of zeros = C/A

=> αß = k/1

=> k = αß

=> k = 3×(-7)

=> k = -21

Hence,

The required value of k is (-21)