Question

If one zero of quadratic polynomial x2 - x - k is the square of other, then find k​

Answer 1

Answer:

Step-by-step explanation:

given,

x^2-x-k = polynomial

let the roots be a,b

given,

a=b^2

sum of roots= -b/a

a +a^2 =1

a^2+a-1=0

a= (-1+(5)^1/2)/2 , -1-(5)^1/2/2

as a has 2 values product of roots is( -1)^2 -5/4

so k is 1-5/4 is -1

Answer 2

Answer:

The values of k are $0$ and $-1$.

Step-by-step explanation:

Given:-

The one of the zero of the quadratic polynomial $x^2-x-k$ is the square of other.

To find:-

The value of k.

Step 1 of 1

Consider the given quadratic equation as follows:

$x^2-x-k=0$

Here, $a = 1, b = -1$ and $c = -k$.

Let the zeros of the polynomial be α and β such that α = β².

As we know,

The sum of zeros is,

α + β = -b/a

β² + β = -(-1)/1

β(β + 1) = 1

$\beta=1$ and $(\beta+1)=1$

⇒ β = 1 and β = 0

The product of zeros is,

β²β = c/a

$\beta^3$ = -k/1

$\beta^3$ = -k . . . . . (i)

For β = 1, the value of k is,

-k = $1^3$

-k = 1

k = -1

For β = 0, the value of k is,

-k = $0^3$

-k = 0

k = 0

Final answer: The values of k are $0$ and $-1$.

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