Question

if alpha and beta are zeroes of 2x^2-3x+1 find alpha^2 and beta^2

Answer 1

Answer:

α² = 1 and β² = 1/4

Step-by-step explanation:

Given :

α and β are the zeroes of the polynomial 2x² - 3x + 1

To find :

the value of α² and β²

Solution :

Let's find the zeroes of the polynomial first and then get the value of α² and β² by substituting.

Finding the zeroes by splitting middle term, [ sum-product pattern ]

2x² - 3x + 1 = 0

2x² - 2x - x + 1 = 0

2x(x - 1) - 1(x - 1) = 0

 (x - 1) (2x - 1) = 0

• x - 1 = 0 ; x = +1
• 2x - 1 = 0 ; x = 1/2

The zeroes of the given polynomial are 1 and 1/2.

Let

• α = 1
• β = 1/2

So,

α² = 1² = 1

β² = (1/2)² = 1/4

______________________________

Know about Quadratic Polynomial :  

✯ It is a polynomial of degree 2  

✯ General form :  

  ax² + bx + c  = 0  

✯ Determinant, D = b² - 4ac  

✯ Based on the value of Determinant, we can define the nature of roots.  

D > 0 ; real and unequal roots  

D = 0 ; real and equal roots  

D < 0 ; no real roots i.e., imaginary  

✯ Relationship between zeroes and coefficients :  

 ✩ Sum of zeroes = -b/a

 ✩ Product of zeroes = c/a