Question

If alpha and Beta are the zeroes of 2x2-5xt+3, find the values of alpha square+beta square​

Answer 1

Step-by-step explanation:

Given -

• α and β are zeroes of polynomial p(x) = 2x² - 5x + 3

To Find -

• Value of α² + β²

Now,

→ 2x² - 5x + 3

By middle term splitt :-

→ 2x² - 2x - 3x + 3

→ 2x(x - 1) - 3(x - 1)

→ (2x - 3)(x - 1)

Zeroes are -

→ 2x - 3 = 0 and x - 1 = 0

→ x = 3/2 and x = 1

Then,

The value of α² + β² is

→ (3/2)² + (1)²

→ 9/4 + 1

→ 9+4/4

→ 13/4

Hence,

The value of α² + β² is 13/4

Answer 2

$\underline{ \underline{ \large{ \bf{ \pink{given}}}}}$

α and β are zeroes of 2 x² - 5 x + 3

$\underline{ \underline{ \large{ \bf{ \pink{ to \: find}}}}}$

α² + β² = ?

$\underline{ \underline{ \large{ \bf { \pink{solution}}}}}$

As we know

$\boxed{ \tt{sum \: of \: zeroes = \frac{ - coefficient \: of \: x}{coefficient \: of \: {x}^{2} } }}$

so,

α + β = -(-5)/2 = 5 / 2

also,

$\boxed{ \tt{product \: of \: zeroes = \frac{constant \:term }{coefficient \: of \: {x}^{2} } }}$

so,

αβ = 3 / 2

Now

we have to find

α² + β²

using identity

x²+y² = (x+y)² - 2xy

α² + β² = ( α+β )² - 2 αβ

putting values

α² + β² = (5/2)² - 2(3/2)

α² + β² = (25/4) - 3

taking LCM

α² + β² = (25 - 12) / 4

$\boxed{ \bf{ { \alpha }^{2} + { \beta }^{2} = \frac{13}{4} }}$