Question

Please give answer with explanation: Q)if alpha and beta are the roots of the equation x 2 + px – 3 = 0 and alpha^2 + beta^ 2 = 10, then p =

Answer 1

Answer:

p = ±2 is the answer for the given problem

Answer 2

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

• p(x) = x² + px - 3
• α² + β² = 10

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

• Value of p

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

p(x) = p(x) = x² + px - 3

• a = 1
• b = p
• c = -3

• ≫ Sum of zeroes = -b/a

↬α + β = -p/1

↬α + β = -p

• ≫ Product of zeroes = c/a

↬αβ = -3/1

↬αβ = -3

Value of α² + β² is 10

we know that,

• ≫ (a + b)² = a² + b² + 2ab

↬(α + β)² = α² + β² + 2αβ

↬ (α + β)² - 2αβ = α² + β²

↬α² + β² = (α + β)² - 2αβ ....(i)

Putting value of (α + β) , α² + β² and αβ in (i)

»» α² + β² = (α + β)² - 2αβ

»» 10 = (-p)² - 2 × (-3)

»» 10 = p² + 6

»» 10 - 6 = p²

»» 4 = p²

»» p = ±√4

»» p = 2 or - 2

So,

✝️Value of p = 2 or -2.

$\rule{200}3$