Question

if alpha and beta are the zeros of a polynomial x square - 7 x + K such that Alpha minus beta is equal to 1 then find the value of k​

Answer 1

Answer : k = 12

Solution :

Given polynomial is

    f(x) = x² - 7x + k

Since α and β are the zeroes of f(x), by the relation between zeroes and coefficients, we get

    α + β = - (- 7/1) = 7

    αβ = k

Given, α - β = 1

Squaring both sides, we get

  (α - β)² = 1²

⇒ (α + β)² - 4αβ = 1

⇒ (- 7)² - 4k = 1

⇒ 49 - 4k = 1

⇒ 4k = 49 - 1 = 48

⇒ k = 48/4

∴ k = 12

Answer 2

K is 12.

K is 12.From the given quadratic equation, we can see that alpha + beta = 7. alpha - beta = 1 is given.

K is 12.From the given quadratic equation, we can see that alpha + beta = 7. alpha - beta = 1 is given.Let me use alpha as a and beta as b.

K is 12.From the given quadratic equation, we can see that alpha + beta = 7. alpha - beta = 1 is given.Let me use alpha as a and beta as b.(a+b)^2 -4ab = (a-b)^2.

K is 12.From the given quadratic equation, we can see that alpha + beta = 7. alpha - beta = 1 is given.Let me use alpha as a and beta as b.(a+b)^2 -4ab = (a-b)^2.Substituting a+b = 7, a-b = 1, we get

K is 12.From the given quadratic equation, we can see that alpha + beta = 7. alpha - beta = 1 is given.Let me use alpha as a and beta as b.(a+b)^2 -4ab = (a-b)^2.Substituting a+b = 7, a-b = 1, we get4ab = 48

K is 12.From the given quadratic equation, we can see that alpha + beta = 7. alpha - beta = 1 is given.Let me use alpha as a and beta as b.(a+b)^2 -4ab = (a-b)^2.Substituting a+b = 7, a-b

Let me use alpha as a and beta as b.

Let me use alpha as a and beta as b.(a+b)^2 -4ab = (a-b)^2.

Let me use alpha as a and beta as b.(a+b)^2 -4ab = (a-b)^2.Substituting a+b = 7, a-b = 1, we get

Let me use alpha as a and beta as b.(a+b)^2 -4ab = (a-b)^2.Substituting a+b = 7, a-b = 1, we get4ab = 48

Let me use alpha as a and beta as b.(a+b)^2 -4ab = (a-b)^2.Substituting a+b = 7, a-b = 1, we get4ab = 48ab = 12.

Let me use alpha as a and beta as b.(a+b)^2 -4ab = (a-b)^2.Substituting a+b = 7, a-b = 1, we get4ab = 48ab = 12.Therefore we can clearly see that k = 12