Question

If x and y are the zeros of the polynomials f(q)=q2-q-1,then what is the value of x2-y2?

Answer 1

Answer:

√5

Step-by-step explanation:

Given that ;

x and y are the zeroes of the polynomial f(q) = q² - q - 1.

On comparing the given equation with ax² + bx + c, we get -

• a = 1
• b = -1
• c = - 1

Sum of zeroes = -b/a

⇒ x + y = -(-1)/1

⇒ x + y = 1 .... (i)

Product of zeroes = c/a

⇒ xy = - 1/1

⇒ xy = - 1

Now, find (x - y) -

We know that ;

(x - y)² = x² + y² - 2xy

⇒ (x - y)² = (x + y)² - 4xy

Substituting the value of above here,

⇒ (x - y)² = (1)² - 4(-1)

⇒ (x - y)² = 1 + 4

⇒ (x - y)² = 5

⇒ (x - y) = √5.... (ii)

Now, we have to find (x² - y²)-

We know that;

x² - y² = (x + y) (x - y)

⇒ x² - y² = 1 * √5

⇒ x² - y² = √5

Hence, the answer is √5.