Question

If alpha and beta are zeroes of quadratic polynomial x2- kx+ 15 Such that (alpha + beta)^2 -2ab = 34, find k

Answer 1

Answer:

± 8

Step-by-step explanation:

Polynomials written in form of x^2 - Sx + P represent S as sum of their roots and P as product of their roots.

Here, if α and β are roots:

    α + β = k

    αβ = 15

In question:

⇒ ( α + β )^2 - 2αβ = 34

 Substituting value from above:

⇒ ( k )^2 - 2( 15 ) = 34

⇒ k^2 - 30 = 34

⇒ k^2 = 34 + 30

⇒ k^2 = 64

⇒ k = ±√64 = ±8

  Hence the required values of k are 8 and - 8

Answer 2

GIVEN THAT:

• Alpha and beta are zeroes of quadratic polynomial x2- kx+ 15.

• (alpha + beta)^2 -2alpha*beta = 34

TO FIND:

• Value of k.

FORMULA USED:

• For a quadratic equation f(x) = ax^2+bx+c = 0 having roots as p and q, we have

p+q = -b/a

p*q = c/a.

SOLUTION:

For x^2-kx+15 with roots alpha and beta, we have

alpha+beta = k...(1)

alpha*beta = 15...(2)

Putting (1) and (2) in (alpha + beta)^2 -2alpha*beta = 34, we get

k^2 -2(15) = 34

k^2 - 30 = 34

k^2 = 64

k = 8 or -8

So, k will be +8 and -8.

Hope this helps