Question

Find α-² + β-², if α and β are zeroes of polynomial 2x² - x + 5.​

Answer 1

Correct Question

⇒Find α² + β² , If α and β are zeroes of polynomial is 2x² - x + 5

Solution

Given Equation

⇒2x² - x + 5 = 0

To find

⇒α² + β²

Now we know that

⇒Sum of zeroes = -b/a

⇒product of zeroes = c/a

Where

⇒a = 2 , b= -1 and c = 5

Put the value on formula

Sum of zeroes

⇒α+β = -(-1)/2 = 1/2

Product of zeroes

⇒αβ = 5/2

Now we have to find

⇒α² + β² = (α + β)² - 2αβ

Put the value on formula

⇒α² + β² = (1/2)² - 2×5/2

⇒α² + β² = 1/4 - 5

⇒α² + β² =( 1 - 5×4)/4

⇒α² + β² = (1-20)/4

⇒α² + β² = -19/4

Answer

⇒α² + β² = -19/4