Question

If P ,Q are the zeros of the quadratic polynomial ( 4x^2 - 4x + 1 ) then ( P^3. + Q^3 ) is​

Answer 1

Answer:-

Given:

P , Q are the zeroes of 4x² - 4x + 1.

On comparing with standard form of a quadratic equation i.e., ax² + bx + c

Let,

• a = 4
• b = - 4
• c = 1.

We know that,

Sum of the zeroes = - b/a

⟶ P + Q = - ( - 4)/1

⟶ P + Q = 4 -- equation (1).

Product of the zeroes = c/a

⟶ PQ = 1/4 -- equation (2)

We know that,

(a + b)³ = a³ + b³ + 3ab(a + b).

⟶ (P + Q)³ = P³ + Q³ + 3PQ(P + Q)

Putting the values from equations (1) & (2) we get,

⟶ (4)³ = P³ + Q³ + 3* (1/4) * (4)

⟶ 64 = P³ + Q³ + 3

⟶ 64 - 3 = P³ + Q³

⟶ 61 = P³ + Q³

Hence, the value of P³ + Q³ is 61.