if alpha ,beta are the roots of quadratic equation 2x square minus 3x

1.	if alpha ,beta are the roots of quadratic equation 2x square minus 3x plus 4 equals to 0 then find. 1. 1 divided by alpha square plus 1 divided by beta square
Answer» $\large\bf\underline {To \: find:-}$ we need to find the value of 1/α² + 1/β² $\huge\bf\underline{Solution:-}$ $\bf\underline{\red{Given:-}}$ ❥ α and β are the roots of the given EQUATION 2x² - 3X + 4 . ● a = 2 ● b = -3 ● c = 4 ☘️ we know that :- → α + β = -b/a → α + β = -(-3)/2 → α + β = 3/2 .....1) → αβ = c/a → αβ = 4/2 → αβ = 2 .......2) ▶Now , FINDING Value of 1/α² + 1/β² :-- → 1/α² + 1/β² → (β² + α²)/(αβ)² ......3) we know that, → a² + b² = (a + b)² - 2ab .....4) ● Now , from 1) , 2) , 3) and 4) → 1/α² + 1/β² = [( α + β)² - 2αβ]/(αβ)² → 1/α² + 1/β² = [(3/2)² - 2 × 2]/2² → 1/α² + 1/β² = [ 9/4 - 4 ]/4 → 1/α² + 1/β² = [ (9 - 16)/4]/4 → 1/α² + 1/β² = -7/4/4 → 1/α² + 1/β² = -7/4 × 1/4 → 1/α² + 1/β² = -7/16 Hence, ༒ Value of 1/α² + 1/β² is -7/16 ━━━━━━━━━━━━━━━━━━━━━━━━━

if alpha ,beta are the roots of quadratic equation 2x square minus 3x plus 4 equals to 0 then find. 1. 1 divided by alpha square plus 1 divided by beta square

Answer»

$\large\bf\underline {To \: find:-}$

we need to find the value of 1/α² + 1/β²

$\huge\bf\underline{Solution:-}$

$\bf\underline{\red{Given:-}}$

❥ α and β are the roots of the given EQUATION 2x² - 3X + 4 .

● a = 2

● b = -3

● c = 4

☘️ we know that :-

→ α + β = -b/a

→ α + β = -(-3)/2

→ α + β = 3/2 .....1)

→ αβ = c/a

→ αβ = 4/2

→ αβ = 2 .......2)

▶Now , FINDING Value of 1/α² + 1/β² :--

→ 1/α² + 1/β²

→ (β² + α²)/(αβ)² ......3)

we know that,

→ a² + b² = (a + b)² - 2ab .....4)

● Now , from 1) , 2) , 3) and 4)

→ 1/α² + 1/β² = [( α + β)² - 2αβ]/(αβ)²

→ 1/α² + 1/β² = [(3/2)² - 2 × 2]/2²

→ 1/α² + 1/β² = [ 9/4 - 4 ]/4

→ 1/α² + 1/β² = [ (9 - 16)/4]/4

→ 1/α² + 1/β² = -7/4/4

→ 1/α² + 1/β² = -7/4 × 1/4

→ 1/α² + 1/β² = -7/16

Hence,

༒ Value of 1/α² + 1/β² is -7/16

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