Question

If α and β are zeroes of y² + 5y + m, find the value of m such that (α + β)² – αβ = 24.

Answer 1

Answer:

m = 1

Step-by-step explanation:

Given :

• α and β are zeroes of y² + 5y + m
• (α + β)² – αβ = 24

Comparing the given polynomial with ax² + bx + c

• a = 1
• b = 5
• c = m

Sum of zeroes = α + β = - b/a = - 5/1 = - 5

Product of zeroes = αβ = c/a = m/1 = m

(α + β)² - αβ = 24

( - 5 )² - m = 24

25 - m = 24

25 - 24 = m

m = 1

Therefore the value of m is 1

Answer 2

Answer:

Value of m in y² + 5y + m is 1.

Step-by-step explanation:

Given Polynomial = y² + 5y + m

(α + β)² – αβ = 24

Let α and β be the zeros of polynomial.

In the polynomial :

• a = 1
• b = 5
• c = m

$\longrightarrow$ α + β = –b/a

$\longrightarrow$ α + β = –5/1

$\longrightarrow$ α + β = –5

___________________________

$\longrightarrow$ αβ = c/a

$\longrightarrow$ αβ = m/1

$\longrightarrow$ αβ = m

___________________________

★ (α + β)² – αβ = 24

$\longrightarrow$ (α + β)² – αβ = 24

$\longrightarrow$ (–5)² – m = 24

$\longrightarrow$ 25 – m = 24

$\longrightarrow$ –m = 24 – 25

$\longrightarrow$ –m = –1

$\longrightarrow$ m = 1

Value of m = 1

Therefore, value of m in y² + 5y + m is 1.