Q4 of 242 Page 8

For what value of k, , is a perfect square.


For the above expression to be a perfect square, D = b2 – 4ac = 0


⇒ (2k + 4)2 – 4 × (4 – k)(8k + 1) = 0


⇒ 4k2 + 16k + 16 + 32k2 – 124k – 16 = 0


⇒ 36k2 – 108k = 0


⇒ 36k(k – 3) = 0


⇒ k = 0, 3


More from this chapter

All 242 →
2

Find the values of k for which the roots are real and equal in each of the following equations:

(i)


(ii)


(iii)


(iv)


(v)


(vi)


(vii)


(viii)


(ix)


(x)


(xi)


(xii) x2 – 2kx + 7x + 1/4 = 0


(xiii)


(xiv)


(xv)


(xvi)


(xvii)


(xviii)


(xix)


(xx)


(xxi)


(xxii)


(xxiii)


(xxiv)


(xxv)


(xxvi)

3

In the following, determine the set of values of k for which the given quadratic equation has real roots:

(i)


(ii)


(iii)


(iv)


(v)


(vi)


(vii)


(viii)


(ix)

5

Find the least positive value of k for which the equation has real roots.

 6

Find the values of k for which the given quadratic equation has real and distinct roots:

(i)


(ii)


(iii)