Question

plz answer this question. ​

Answer 1

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Answer 2

Given Polynomial :-

y² - 2y - 7 = 0

Here , Coefficient of y² (a) = 1

Coefficient of y (b) = -2

Constant term (c) = -7

It's zeros are given according to the question that are :- Alpha and Beta

Now , We know that ,

Product of the zeros = Constant term/Coefficient of y²

or

Product of zeros = c/a

So , Alpha x Beta = -7/1 - {1}

(1)

Sum of the zeros = -(Coefficient of y)/(Coefficient of y²)

or

Sum of the zeros = -b/a

So,

Alpha + Beta = -(-2)/1 - {2}

Squaring both sides:-

(Alpha + Beta)² = (2)²

Alpha² + Beta² + 2 x Alpha x Beta = 4

[ By identity :- (a+b)² = a² + b² + 2ab ]

Alpha² + Beta² + 2 x (-7) = 4 [ From Equation {1} ]

Alpha² + Beta² -14 = 4

Alpha² + Beta² = 14 + 4

Alpha² + Beta² = 18

(2)

Again ,

Sum of the zeros = -b/a

Alpha + Beta = -(-2)/1

Now , Cubing Both Sides :-

(Alpha + Beta)³ = (2)³

Alpha³ + Beta³ + 3 x Alpha x Beta(Alpha + Beta) = 8

[ By identity :- (a+b)³ = a³ + b³ + 3ab(a+b) ]

Alpha³ + Beta³ + 3 x (-7)(2) = 8 [ From Equation {1} and {2} ]

Alpha³ + Beta³ -42 = 8

Alpha³ + Beta³ = 42 + 8

Alpha³ + Beta³ = 50

This is it , hope it helped you...