Question

If α,βare the roots of quadratic polynomial p(x)=x2-(k-6)x+(2k+1) find the value of K if α+β=αβ

Answer 1

.Sol:
Given  α and β are zeroes of the polynomial f(x) = ax2 + bx + c

α+ β = -b / a
αβ = c / a.

If α and β are zeroes of the quadratic polynomial p(x)=x2-(k-6)x+(2k+1) and α+β= αβα+ β = k - 6 and  αβ = 2k + 1

Given that    α + β = αβ

k - 6 = 2k + 1

∴ k = - 7 .

Answer 2

Hey dear !!!

___________________________

==> In the example

p(x) = x² - (k-6)x + (2k + 1)

We have given that,

α + β = αβ

We have ;

a = 1
b = -(k-6)
c = (2k + 1)

We know that,

α + β = -b/a = -(-k-6) = k - 6

αβ = c/a = 2k+1

According to the given condition ,

α + β = αβ

κ - 6 = 2k + 1

k - 2k = 1 + 6

- k = 7 .........(multiplying by -1 on both side we get)

k = -7

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