Question

Plz its humble request from me tell me correct answer and explain​

Answer 1

Answer:

c) 3/2

Step-by-step explanation:

Let, the roots are α and β

so, α + β = $\frac{-b}{a}$ and αβ =  $\frac{c}{a} (for -//ax^2+bx +c)$

here  α + β = $\frac{2(k-2)}{2}$ = k-2

and  αβ = $\frac{-(k+1)}{2}$

now, α² + β² = (α + β)² - 2αβ = (k-2)² + k+1 = k²+4 -4k +k +1  = k² -3k +5

differentiate to get the minimum value

$\frac{d}{dk}(k^2 -3k +5)$ = 0

► 2k - 3 = 0

► k= 3/2

Answer 2

Step-by-step explanation:

Let, the roots are α and β

so, α + β = \frac{-b}{a}

a

−b

and αβ = \frac{c}{a} (for -//ax^2+bx +c)

a

c

(for−//ax

2

+bx+c)

here α + β = \frac{2(k-2)}{2}

2

2(k−2)

= k-2

and αβ = \frac{-(k+1)}{2}

2

−(k+1)

now, α² + β² = (α + β)² - 2αβ = (k-2)² + k+1 = k²+4 -4k +k +1 = k² -3k +5

differentiate to get the minimum value

\frac{d}{dk}(k^2 -3k +5)

dk

d

(k

2

−3k+5) = 0

► 2k - 3 = 0

► k= 3/2