Question

1. If a and ß are the zeroes of the polynomial
ax²+bx+c. find the value of a2
+ B²


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Answer 1

Answer:

Explanation:

Given :

• Quadratic polynomial, ax² + bx + c.

To Find :

• The value of α² + β².

Solution :

Given, quadratic polynomial, ax² + bx + c.

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

=> a = a , b = b, c = c

• Sum of zeroes = -b/a

=> α + β = -b/a

=> α + β = -b/a

• Product of zeroes = -c/a

=> αβ = c/a

=> αβ = c/a

Now,

α² + β² = (α + β)² + 2αβ

=> α² + β² = (-b/a)² + 2(c/a)

=> α² + β² = b²/a² + 2 × c/a

=> α² + β² = b²/a² + 2c/a

=> α² + β² = b² + 2ac/a²

Hence :

The value of α² + β² is b² + 2ac/a².

Answer 2

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Explanation:

Given :

• Quadratic polynomial, ax² + bx + c.

To Find :

• The value of α² + β².

Solution :

Given, quadratic polynomial, ax² + bx + c.

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

=> a = a , b = b, c = c

• Sum of zeroes = -b/a

=> α + β = -b/a

=> α + β = -b/a

• Product of zeroes = -c/a

=> αβ = c/a

=> αβ = c/a

Now,

α² + β² = (α + β)² + 2αβ

=> α² + β² = (-b/a)² + 2(c/a)

=> α² + β² = b²/a² + 2 × c/a

=> α² + β² = b²/a² + 2c/a

=> α² + β² = b² + 2ac/a²

Hence :

The value of α² + β² is b² + 2ac/a².