Question

If alpha and beta are the zeros of quadratic polynomial X square + X - 2 find the value of one upon Alpha minus one upon beta

Answer 1

Answer:

3/2

Step-by-step explanation:

Given that α and β are the zeroes of the given polynomial.

$\bigstar$ p(x) = x² + x - 2

Solving it further by Middle Term Factorisation.

→ p(x) = x² + 2x - x - 2

→ p(x) = x(x + 2) - 1(x + 2)

→ p(x) = (x - 1)(x + 2)

To find the zeroes, we use zero product rule.

→ (x - 1) = 0 and (x + 2) = 0

→ x = 1 and x = - 2

A.T.Q., α = 1 and β = - 2

Now,

To Find : ${\sf{ {\dfrac{1}{ \alpha}} - {\dfrac{1}{ \beta}} }}$

Putting the known values, we get

→ ${\sf{ {\dfrac{1}{(1)}} - {\dfrac{1}{(- 2)}} }}$

→ ${\sf{ {\dfrac{1}{1}} + {\dfrac{1}{2}} }}$

→ ${\sf{ {\dfrac{2 + 1}{2}} }}$

→ ${\sf{\red{ {\dfrac{3}{2}} }}}$

Hence, the required value is 3/2.

Answer 2

$\large{\underline{\underline{\mathfrak\red{Question\::}}}}$

If alpha and beta are the zeros of quadratic polynomial x² + x - 2 find the value of one upon Alpha minus one upon beta

$\large{\underline{\underline{\mathfrak\green{SOLUTION\::}}}}$

$\implies$ p(x)= x² -x -2 (given)

$\implies$ [where , a = 1 , b = 1 ,c = -2]

$\implies$ sum of zeroes = -b/a

$\implies$ α + β = -1/1

$\implies$ $\red{\boxed{α + β = -1}}$

$\implies$ product of zeroes = c/a

$\implies$ α × β = -2 / 1

$\implies$ $\green{\boxed{α × β = -2}}$

NOW,

$\implies$1/α - 1/β = β - α /αβ

$\implies$√(α +β)²-4αβ / -(αβ)

$\implies$ √(-1)²-4(-2)/-(-2)

$\implies$ √ 1+8/2

$\implies$ √9/2

$\implies$ $\blue{\boxed{3/2}}$

SO, the value of one upon Alpha minus one upon beta is 3/2.