Question

If if A and B are zeros of the polynomial x square - 11 x + 30 find the value of a cube plus b cube

Answer 1

Question

If if A and B are zeros of the polynomial x² - 11 x + 30 find the value of a cube plus b cube

Solution

Given :-

• Equation , x² - 11x + 30 = 0
• A & B are zeroes of this equation

Find :-

• Value of A³ - B³

Explanation

Using Formula

★(p+q)² = p² + q² + 2pq

★(p-q)² = p² + q² -2pq

★(p³-q³ = (p-q)(p²+q²+pq)

★ Sum of zeroes = -(Coefficient of x)/(coefficient of x²)

★product of zeroes = (constant part)/(coefficient of x²)

So,

==> Sum of zeroes = -(-11)/1

==> A + B = 11 ------------(1)

And,

==> product of zeroes = 30/1

==> AB = 30 ------------(2)

Squaring both side of equ(1)

==> (A+B)² = 11²

==> A² + B² + 2AB = 121

Keep Value by equ(2)

==> A² + B² = 121 - 2*30

==> A² + B² = 121 - 60

==> A² + B² = 61 ------------(3)

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Now,

★ (A - B ) = √[(A+B)² -4AB]

Keep Value by equ(1) & equ(2)

==> A - B = √[(11)²-4*30]

==> A - B = √[121-120]

==> A - B = √(1)

==> A - B = 1 -------------(4)

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Now, Calculate

==> (A³ - B³) = (A-B)(A² + B² +AB)

Keep Value by equ(2),(3) & (4)

==> (A³ - B³) = (1) * (61 + 30)

==> (A³ - B³) = 91

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Hence

• Value of (A³ - B³) = 91

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