Question

if alpha and beta are zeroes of polynomial 4x^2+3x+7,so find the value (i) alpha^2+beta^2​

Answer 1

Answer:

α² + β² is –47/16.

Step-by-step explanation:

Given Polynomial = 4x² + 3x + 7

Value of α² + β² = ??

In the polynomial,

• a = 4
• b = 3
• c = 7

Sum of zeros -

$\longrightarrow$ α + β = –b/a

$\longrightarrow$ α + β = –3/4

Product of zeros -

$\longrightarrow$ αβ = c/a

$\longrightarrow$ αβ = 7/4

★ Value of α² + β² :

$\longrightarrow$ α² + β²

$\longrightarrow$ (α + β)² – 2αβ

$\longrightarrow$ (–3/4)² – 2(7/4)

$\longrightarrow$ 9/16 – 7/2

$\longrightarrow$ 9/16 – 56/16

$\longrightarrow$ –47/16

Therefore, α² + β² is –47/16.

Answer 2

Answer:

In the polynomial,

a = 4

b = 3

c = 7

Sum of zeros -

$\longrightarrow$ α + β = –b/a

$\longrightarrow$ α + β = –3/4

Product of zeros -

$\longrightarrow$ αβ = c/a

$\longrightarrow$ αβ = 7/4

now Value of α² + β² :

$\longrightarrow$ α² + β²

$\longrightarrow$ (α + β)² – 2αβ

$\longrightarrow$ (–3/4)² – 2(7/4)

$\longrightarrow$ 9/16 – 7/2

$\longrightarrow$ 9/16 – 56/16

$\longrightarrow$ –47/16