Question

find the value of k, if one root of the equation x2-6x+k=0 is square of the other root​

Answer 1

Let r be the lesser root and r^2 be the greater.......

the sum of the roots =

$-b/a = -[-6] / 1 = 6$

So we have that

$r^2 + r = 6 → r^2 + r - 6 = 0$

Factor

$(r + 3) (r - 2) = 0 </p><p></p><p>So r = -3 or r = 2</p><p>$

Then

$r^2 = 9 or r^2 =4$

And the product of the roots =

$c/a = k/a = k$

So....

$k = (-3)(9) = -27 or k = (2)(4) = 8$

Check

$x^2 - 6x - 27 = 0$

factors as

$(x + 3)(x - 9) = 0$

and the roots are -3 and 9

$x^2 - 6x + 8 = 0$

factors as $(x -2) (x - 4) =0$

and the roots are

$2$

and

$4$

hope it's help you ✔️