C1 Completing Square

(a) By completing the square, find in terms of k the roots of the equation

x2 + 2kx – 7 = 0. (4)

(b) Prove that, for all values of k, the roots of x2 + 2kx – 7 = 0 are real and different.
(2)

(c) Given that k = root2, find the exact roots of the equation.

Hi. im stuck on this , if sum1 cud post the completin square rule as well as answerin it wud help me in future :smile:

rep given

Reply 1

yazan_l

a) x² + 2kx – 7 = 0
x² + 2kx + k² - k² – 7 = 0
(x + k)² - (k²+7) = 0
(x + k)² = (k²+7)
x = (k²+7)^½ - k

b) k²+7 is always +ve, i.e. its square root is always real. hence x is always real. and as any value of k has only one value of x ==> the roots are always real and different!

Edit: forgot part c:
c) just substitute k = root2
x = 3-root2