Question

If one root of x2 - x - k = 0 is twice the other then what is the value of k ?
Full Answer please. ​

Answer 1

Answer :-

Let the root of quadratic equation x^2 - x - k be a and 2a

As we know , quadratic equation can be expressed in form ax^2 + bx + 0 =0 and α and β are the roots

.

α + β = -b / a

α * β = c / a

Here, a = 1 , b = -1 and c = -k and a and 2a are the roots

Sum of zeroes = -b/a

a + 2a = -(-1)/1

3a = 1

a = 1/3 .........eq(1)

Product of zeroes = c/a

a * 2a = -1/1 .......eq(2)

Subsitute eq( 1) in eq(2)

1/3 * 2 * 1/3 = -k/1

1/3 * 2/3 = -k

k = -2/9

The value of K = -2 / 9