Question

If a, ß are zeroes of the polynomial
p(x) = x² – 3ax + a², then the value of a if it is given that a² + ß² = 7/4 is?
​

Answer 1

Answer :

• a = 1/2

S O L U T I O N :

Given,

• α and β are the zeroes of the polynomial.

• Polynomial, p(x) = x² - 3ax + a² = 0.

• α² + β² = 7/4

To Find,

• The value of a.

Explanation,

Given, Polynomial, p(x) = x² - 3ax + a² = 0.

On comparing with, ax² + bx + c = 0, We get ;

=> a = 1 , b = -3a , c = a²

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

=> Sum of roots = -b/a

=> α + β = -(-3a)/1

=> α + β = 3a

=> Product of roots = c/a

=> αβ = a²/1

=> αβ = a²

Given, α² + β² = 7/4

We know that,

α² + β² = (α + β)² - 2αβ

[ Put the values ]

=> 7/4 = (3a)² - 2(a²)

=> 7/4 = 9a² - 2a²

=> 7/4 = 7a²

=> a² = 1/4

=> a = √1/4

=> a = 1/2

Therefore,

The value of a is 1/2.