Question

If alpha and beeta are zeroes of polynomial 2x²+7x+5 than find the value of alpha and beeta, alpha +beeta

Answer 1

Step-by-step explanation:

Given equation:- 2x² - 7x + 5 = 0

Let's factorise it by middle term splitting !!

2x² - 7x + 5 = 0

2x² - 2x - 5x + 5 = 0

2x ( x - 1 ) - 5 ( x - 1 ) = 0

( 2x - 5 ) ( x - 1 ) = 0

• ( 2x - 5 ) = 0

x = 5/2

• ( x - 1 ) = 0

x = 1

so \: \: \alpha = \frac{5}{2} \: \: \:and \: \: \beta =1

• Zeros of new polynomial are :-

2 \alpha + \beta \: \: \: and \: \: 2 \beta + \alpha

( ur question have an error the second Zeros will be 2beta + alpha )

2 \alpha + \beta = 2 \times \frac{5}{2} + 1 = 5 +1 = 6

2 \beta + \alpha = 2 \times 1 + \frac{5}{2} = \frac{4 + 5}{2} = \frac{9}{2}

• Sum of Zeros :-

6 + \frac{9}{2} = \frac{12 + 9}{2} = \frac{21}{2}

• Product of Zeros :-

6 X 9 / 2= 27

♯ To form the quadratic equation we have formula as :-

x² - ( Sum of Zeros )x + (Product of Zeros)

Putting value in it !!

{x}^{2} - \frac{21}{2} x + 27 = 0

\frac{2{x}^{2} - 21x +54 }{2} = 0

2x² - 21x + 54 = 0 is the required quadratic equation !!