Question

if alpha and beta are the zeros of the given polynomial p(x) = 4x^2 - x - 4 . find alpha ^3 + beta^3
(class 10th maths chapter polynomial) ​

Answer 1

To Find :-

• The value of α³ + β³.

Solution :-

Given,

• α and β are the zeroes of quadratic polynomial.

• Quadratic polynomial ; p(x) = 4x² - x - 4.

Given, p(x) = 4x² - x - 4

On comparing with ax² + bx + c , We get ;

↪ a = 4 , b = -1 , c = -4

Given, α and β are the zeroes of quadratic polynomial.

Sum of roots = -b/a

↪ α + β = -(-1)/4

↪ α + β = 1/4

Product of roots = c/a

↪ αβ = -4/4

↪ αβ = -1

Now, we need find the value of α³ + β³.

We know that,

α³ + β³ = (α + β)³ - 3αβ(α + β)

[ Put the values ]

↪ α³ + β³ = (1/4)³ - 3(-1)(1/4)

↪ α³ + β³ = 1/64 + 3 × 1 × 1/4

↪ α³ + β³ = 1/64 + 3/4

↪ α³ + β³ = 49/64

Therefore,

The value of α³ + β³ is 49/64.