Question

Answer the question 15
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Answer 1

Answer:

a =  - 4(√3 + 1)

Step-by-step explanation:

For equation x² - (√3 + 1)x + k = 0, let 1 and α be the roots.

a = 1, b = -(√3 + 1), c = k

product of roots = 1 * α = c/a = k => α = k.

Sum of roots = 1 + α = -b/a = -( -(√3 + 1))/1 = (√3 + 1)

=> α = (√3 + 1) - 1 = √3.

Since α = k, k = √3

Now the equation becomes 4x² + 4kx + a = 0 => 4x² + 4√3x + a = 0

Let 1 and β be the roots of this equation.

A = 4, B = 4√3, C = a.

product of roots = 1 * β = C/A = a/4.

Sum of roots = 1 + β = -B/A = - 4√3/4 = - √3.

=> β = - (√3 + 1)

But β = a/4

=> a/4 = - (√3 + 1)

=> a =  - 4(√3 + 1)