Question

The value for which the sum of squares of root of 2 x 2-2(a-2)x

Answer 1

Answer:

Step-by-step explanation:

A quadratic equation is of the form,

x^2 - (sum of roots)x + (product of roots) = 0

Here,

Sum of roots = a-2

product of roots = -a-1

Let the roots of the equation be p and q

p+q = a-2

p*q = -a-1

(p+q)^2 = (a-2)^2

p^2 + q^2 + 2pq = a^2 + 4 -4a

p^2 + q^2 = a^2 + 4 - 4a - 2pq

sum of squares of roots = a^2 + 4 -4a - 2(-a-1)

=a^2 +6 -2a

d/dt(a^2 + 6 -2a) = 0 [at minimum value of a]

2a - 2 = 0

a = 1