Question

if the difference of the roots of the quadratic equation X square + kx + 12 equal to zero is 1 then find the positive value of k

Answer 1

Answer:

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Answer 2

Given,

The quadratic equation x² + kx + 12=0 and the difference of the roots of the quadratic equation is 1.

To find,

The value of k.

Solution,

• The sum and the products of the roots of the equation ax²+bx+c=0 is given by-

        α+β = -b/a

        αβ = c/a

• Similarly, the sum and the products of the roots of the equation x² + kx + 12=0 is given by-

        α+β = -k

        αβ = 12

It is given to us that α-β =1

⇒(α-β)²=(α+β)²-4αβ

⇒   (1)²=(-k)²-4(12)

⇒   1 = k²-48

⇒   1 + 48 = k²

⇒   49 = k²

⇒    k = 7 or k = -7.

Hence, the value of k is 7 or -7.